Equation 677 Database

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Magma a497700da7a0…

magma a497700da7a0
Size
735
Isomorphism class hash
a497700da7a0850c338f1c973ea1403ef4c0db8c37a12e9e3259db8c594ba81c
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 105 (nullity 630) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 21:38:30
Display reorder
625,616,605,626,629,603,624,617,604,622,618,602,623,619,601,621,620,600,608,612,609,610,607,611,615,627,606,613,628,614,730,734,732,733,731,41,569,568,570,565,572,358,111,571,576,574,573,575,566,577,359,109,371,581,579,578,580,564,582,357,110,40,586,583,584,585,567,587,355,114,43,598,595,596,597,593,599,356,112,44,591,589,588,590,594,592,354,113,42,125,100,9,103,365,417,363,344,521,117,123,101,10,104,366,418,364,342,522,115,102,124,8,105,367,416,362,343,523,116,106,6,372,414,368,122,120,524,347,373,107,7,121,98,369,415,361,118,525,345,409,99,527,108,370,413,360,119,526,346,97,95,93,94,92,96,700,698,697,699,696,701,654,651,652,650,655,656,653,709,703,705,702,710,729,704,158,28,457,65,15,75,29,49,73,74,26,456,63,16,76,30,50,159,72,27,458,64,14,77,31,48,160,70,25,459,68,12,78,32,46,161,71,23,460,66,13,79,33,47,162,69,24,461,67,11,80,34,45,163,488,432,451,55,82,166,392,438,381,386,489,433,452,56,83,167,393,515,382,387,431,490,453,54,81,168,391,437,380,385,52,495,389,518,505,486,498,412,441,473,53,449,508,435,85,164,390,384,410,439,487,434,450,51,84,165,388,383,411,440,3,4,2,1,0,5,662,665,664,661,666,663,714,713,716,719,721,718,715,686,681,682,684,688,685,683,309,279,335,293,131,142,337,425,301,299,280,333,291,129,143,338,426,307,300,278,334,292,130,144,336,427,308,298,277,332,296,128,145,340,428,516,506,496,330,294,126,519,341,429,310,297,276,331,295,127,146,339,430,311,349,329,454,509,491,313,442,474,436,444,350,327,135,246,286,314,284,302,137,443,328,348,136,245,287,312,285,303,138,445,243,134,283,316,288,352,446,139,306,326,244,132,353,324,289,317,281,447,140,304,351,325,133,242,290,315,282,448,141,305,323,321,319,320,318,322,667,659,658,657,660,668,708,711,720,717,706,712,707,676,679,678,687,680,677,675,247,257,259,232,20,420,270,149,240,241,258,260,230,21,419,268,147,248,239,256,261,231,22,421,269,148,249,237,254,262,235,17,422,267,152,250,238,255,263,233,18,423,265,150,251,236,253,264,234,19,424,266,151,252,510,470,476,157,402,396,466,482,503,274,511,471,477,155,400,394,467,494,504,275,472,517,475,156,401,395,465,481,502,273,154,499,463,399,405,513,493,507,485,480,497,479,514,468,403,397,464,272,501,483,512,469,478,153,404,398,462,271,500,484,89,90,88,86,87,91,671,673,670,669,674,672,728,722,723,724,725,727,726,695,691,690,693,692,694,689,190,559,529,552,546,536,184,374,541,539,560,528,553,547,537,185,375,191,540,558,530,551,545,538,186,376,189,544,562,531,555,549,533,181,377,520,542,563,557,556,550,534,182,378,188,543,561,532,554,548,535,183,379,187,455,408,218,217,179,196,169,492,228,57,39,406,219,215,180,197,170,204,229,58,407,38,220,216,178,195,171,205,227,59,214,221,172,193,176,36,60,225,206,209,212,222,37,210,177,194,173,61,226,207,35,211,223,213,175,192,174,62,224,208,202,203,198,199,200,201,645,644,646,649,648,647,642,638,641,639,640,643,637,633,632,636,634,635,631,630 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 735 = 35 + 5*140, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#b9de522453e3fa122a64cff43bfc0df3d92e544d29dc14c1457437ec5f7fa4d2, M = the submagma generated by {0, 2} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 105.

last edited by qawbecrdtey at 2026-10-07 21:38:31 · history