Equation 677 Database

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Magma 28991d52c222…

magma 28991d52c222
Size
705
Isomorphism class hash
28991d52c222b615e18684a37bbdf93ad4f8d08764dd2f66669c6506fd8d0c1c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 19:19:26
Display reorder
660,222,377,403,392,91,220,89,375,404,390,221,90,376,402,391,218,380,87,399,388,219,378,88,400,389,217,379,86,401,387,213,372,82,394,383,211,373,80,395,381,212,374,81,393,382,371,216,85,397,386,369,214,83,398,384,370,215,84,396,385,685,686,688,687,131,479,457,448,466,132,467,477,458,449,133,465,478,456,447,130,482,469,453,451,128,480,470,454,452,129,481,468,455,450,137,485,472,463,446,138,483,473,464,444,139,484,471,462,445,488,136,475,459,442,486,134,476,460,443,487,135,474,461,441,701,702,704,703,365,210,600,591,608,363,609,208,601,592,364,610,209,599,590,368,206,611,596,594,366,207,612,597,595,367,205,613,598,593,360,201,614,606,589,361,199,615,607,587,362,200,616,605,588,204,359,617,602,585,202,357,618,603,586,203,358,619,604,584,670,669,672,671,49,6,497,303,141,47,142,7,495,301,48,140,8,496,302,45,9,144,500,306,46,10,145,498,304,44,11,143,499,305,55,4,147,492,298,53,5,148,493,299,54,3,146,494,300,1,51,150,491,297,0,52,151,489,295,2,50,149,490,296,680,677,679,678,58,524,158,317,509,56,507,522,159,318,57,508,523,160,316,61,520,512,161,313,59,521,510,162,314,60,519,511,163,315,64,515,504,156,308,62,513,505,157,309,63,514,506,155,307,518,67,503,152,311,516,65,501,153,312,517,66,502,154,310,689,690,691,692,78,179,332,569,271,79,272,180,333,567,77,273,181,331,568,74,178,274,335,572,75,176,275,336,570,76,177,276,334,571,69,185,277,338,564,70,186,278,339,565,68,187,279,337,566,184,72,280,341,563,182,73,281,342,561,183,71,282,340,562,697,698,700,699,34,626,655,637,24,32,25,627,653,635,33,23,628,654,636,37,629,20,651,633,35,630,21,652,634,36,631,22,650,632,40,624,30,646,643,38,625,31,644,641,39,623,29,645,642,620,43,26,649,639,621,41,27,647,640,622,42,28,648,638,661,662,664,663,228,412,97,422,114,226,115,413,95,420,227,113,411,96,421,224,415,110,93,418,225,416,111,94,419,223,414,112,92,417,234,410,105,103,428,232,408,106,101,426,233,409,104,102,427,406,230,108,99,424,407,231,109,100,425,405,229,107,98,423,682,681,684,683,288,15,580,193,346,286,347,16,578,194,287,348,14,579,195,284,18,345,583,196,285,19,343,581,197,283,17,344,582,198,294,13,352,576,191,292,12,353,577,192,293,657,656,658,659,354,290,351,575,190,355,291,349,573,188,356,289,350,574,189,693,694,696,695,175,319,547,533,551,173,549,320,548,531,174,550,321,546,532,171,322,554,543,536,172,323,552,544,534,170,324,553,545,535,166,325,557,538,528,164,326,555,539,529,165,327,556,537,530,328,169,560,541,527,329,167,558,542,525,330,168,559,540,526,666,665,668,667,440,252,121,269,242,438,243,250,119,270,439,241,251,120,268,436,248,245,117,265,437,249,246,118,266,435,247,244,116,267,431,258,240,127,260,429,256,238,125,261,430,257,239,126,259,254,434,236,123,263,255,432,237,124,264,253,433,235,122,262,674,673,676,675 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#9dc1b7560e7dd8c4d9175d590a741d2999f3578c3e161e058f60df88b07e0ac9, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 19:19:26 · history