Equation 677 Database

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Magma 58113a67fdab…

magma 58113a67fdab
Size
707
Isomorphism class hash
58113a67fdab40d781ae6cdef4f7b642bb83a4d1055dba64949738a402e0348d
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 11:14:38
Display reorder
84,89,85,86,87,88,706,287,283,284,285,286,282,53,52,48,49,50,51,305,304,301,300,302,303,293,292,288,289,290,291,186,191,187,188,189,190,65,64,60,61,62,63,223,227,222,224,225,226,9,8,10,11,6,7,31,30,32,33,34,35,298,299,294,296,297,295,327,329,328,326,324,325,574,573,575,572,571,570,441,443,442,440,438,439,355,354,356,359,357,358,578,576,577,579,580,581,515,514,513,510,511,512,450,452,451,454,455,453,523,522,524,525,526,527,468,470,469,471,472,473,427,426,428,430,431,429,612,610,608,611,606,607,635,630,637,633,683,681,697,698,705,696,699,702,704,703,245,240,242,243,244,241,130,129,131,126,127,128,251,250,247,246,248,249,121,120,122,123,124,125,257,256,253,252,254,255,140,139,141,142,143,138,100,99,101,96,97,98,235,239,234,236,237,238,160,159,161,156,157,158,196,195,197,192,193,194,544,543,545,541,540,542,378,380,379,382,383,381,384,386,385,389,387,388,531,533,532,528,530,529,481,480,482,485,483,484,390,392,391,394,395,393,403,402,404,407,405,406,539,538,537,534,536,535,508,507,509,505,506,504,398,397,396,401,399,400,614,615,618,613,619,617,620,616,631,632,687,700,701,670,686,673,671,675,672,685,279,281,277,276,278,280,102,107,103,104,105,106,213,212,214,215,210,211,208,207,209,204,205,206,27,26,28,29,24,25,216,221,217,218,219,220,119,118,114,115,116,117,56,55,57,58,59,54,137,136,132,133,134,135,23,22,18,19,20,21,314,313,312,316,317,315,320,319,318,321,322,323,558,559,560,561,562,563,376,375,377,374,372,373,423,425,424,421,422,420,584,582,583,585,586,587,489,491,490,487,488,486,568,567,569,565,564,566,553,554,552,555,556,557,446,445,444,449,447,448,625,624,629,626,627,622,634,623,636,628,669,695,692,674,679,682,666,684,667,693,15,17,12,13,14,16,112,111,113,108,109,110,155,154,150,151,152,153,202,201,203,198,199,200,262,261,263,259,258,260,37,36,38,39,40,41,148,147,149,144,145,146,265,269,264,266,267,268,275,274,271,270,272,273,80,79,81,82,83,78,416,415,414,418,419,417,498,500,499,502,503,501,517,516,518,519,520,521,495,497,496,493,494,492,308,306,307,309,310,311,590,588,589,591,592,593,551,550,549,547,546,548,412,411,413,408,409,410,597,599,598,595,594,596,605,604,603,602,601,600,638,649,621,639,651,640,647,653,646,654,676,688,694,680,691,678,668,690,677,689,233,229,230,231,232,228,94,93,95,90,91,92,165,164,166,167,162,163,174,179,175,176,177,178,184,183,185,180,181,182,171,170,172,173,168,169,3,2,4,5,1,0,68,67,69,70,71,66,74,73,75,76,77,72,47,46,42,43,44,45,476,475,474,478,479,477,467,466,465,462,463,464,367,366,368,369,370,371,456,458,457,460,461,459,363,365,364,361,362,360,347,346,345,342,343,344,337,336,338,341,339,340,352,351,353,348,349,350,332,331,330,335,333,334,434,433,432,437,435,436,641,643,650,609,652,645,648,644,642,655,656,659,664,661,660,663,658,662,657,665 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#e4013d0178842fa1abe6ac84eb6d8732370ca50237187a2a953024cf339ab2c2, M = {60, 61, 62, 63, 64, 65, 144} 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 11:14:41 · history