Equation 677 Database

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Magma 43bc81851392…

magma 43bc81851392
Size
707
Isomorphism class hash
43bc8185139274bd75e0ec3cf2effa2b62f3ec1c93523b46b1c186dd8e4ff8bc
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 17:12:11
Display reorder
87,86,88,89,84,85,706,283,284,285,286,287,282,230,229,231,232,233,228,321,320,322,323,318,319,122,121,123,124,125,120,113,112,108,109,110,111,199,198,200,201,202,203,220,219,221,216,217,218,234,239,235,236,237,238,191,190,186,187,188,189,332,330,333,334,335,331,326,325,324,327,328,329,504,503,551,507,505,506,489,488,490,485,486,487,544,546,545,548,549,547,413,415,414,416,417,418,473,475,474,476,477,478,464,466,465,461,462,463,512,511,513,509,510,508,391,390,392,550,393,394,460,459,458,455,456,457,611,606,612,610,613,614,637,635,639,694,666,656,672,696,703,697,698,705,704,700,73,74,75,76,77,72,294,299,295,296,297,298,293,292,288,289,290,291,144,149,145,146,147,148,62,61,63,64,65,60,45,44,46,47,42,43,156,161,157,158,159,160,18,23,19,20,21,22,267,266,268,269,264,265,173,172,168,169,170,171,162,167,163,164,165,166,433,432,431,436,434,435,370,369,371,366,367,368,361,360,362,365,363,364,571,572,570,573,574,575,385,384,386,388,389,387,383,382,381,380,378,379,373,372,374,376,377,375,395,397,396,399,400,398,578,576,577,579,580,581,622,609,615,624,608,607,630,634,633,675,669,664,655,684,687,674,680,695,686,685,103,104,105,106,107,102,185,184,180,181,182,183,92,91,93,94,95,90,13,12,14,15,16,17,26,25,27,28,29,24,100,99,101,96,97,98,8,7,9,10,11,6,69,68,70,71,66,67,32,31,33,34,35,30,317,316,313,312,314,315,279,278,280,281,276,277,552,554,553,555,557,556,565,564,566,567,568,569,442,441,440,437,438,439,336,337,338,340,341,339,445,444,443,448,446,447,430,429,428,427,425,426,423,422,424,420,421,419,560,558,559,561,562,563,583,584,582,586,587,585,627,631,625,626,629,628,638,632,636,681,670,663,662,691,682,690,671,701,676,688,274,275,270,271,272,273,176,175,177,178,179,174,136,135,137,132,133,134,257,256,252,253,254,255,40,39,41,36,37,38,259,258,260,261,262,263,49,48,50,51,52,53,248,247,249,250,251,246,143,142,138,139,140,141,80,79,81,82,83,78,54,59,55,56,57,58,590,588,589,593,591,592,533,532,534,535,536,537,351,353,352,349,350,348,343,342,344,346,347,345,604,603,605,600,602,601,403,402,401,406,404,405,598,597,599,594,596,595,449,451,450,453,454,452,531,530,529,526,527,528,646,644,642,643,640,641,645,648,647,699,667,659,692,693,683,679,677,702,689,678,4,5,1,0,2,3,311,310,307,306,308,309,126,131,127,128,129,130,195,194,196,197,192,193,215,214,210,211,212,213,243,242,244,245,240,241,118,117,119,114,115,116,154,153,155,150,151,152,304,303,305,301,300,302,227,226,222,223,224,225,205,204,206,207,208,209,355,354,356,358,359,357,412,411,410,408,409,407,514,516,515,518,519,517,539,538,540,542,543,541,470,472,471,467,468,469,481,480,479,484,482,483,491,493,492,494,495,496,522,521,520,523,524,525,501,500,502,499,497,498,617,618,620,621,616,619,623,650,649,668,653,651,652,665,661,660,657,673,658,654 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 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#5d364ad3474cdcd7c6d5defafd2fd9bfd394ea971d15e95ed0d16a1c5a75c76d, M = {42, 43, 44, 45, 46, 47, 140} 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: 101.

last edited by qawbecrdtey at 2026-10-06 17:12:12 · history