Equation 677 Database

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Magma 95c9fd3cfec1…

magma 95c9fd3cfec1
Size
705
Isomorphism class hash
95c9fd3cfec16437ed9f3527c3c8030e48924a4c5842ce42c6f52ad55c193a25
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 21:49:11
Display reorder
660,502,501,503,500,498,499,492,493,494,495,496,497,252,253,254,255,256,257,258,259,260,261,262,263,612,613,614,615,616,617,618,619,620,621,622,623,560,558,559,563,561,562,555,556,557,554,552,553,8,6,7,11,9,10,3,4,5,2,1,0,669,683,686,690,279,281,280,277,278,276,287,285,286,283,284,282,352,353,351,348,349,350,358,359,357,354,355,356,473,471,472,469,470,468,479,477,478,475,476,474,147,148,149,146,144,145,153,154,155,152,150,151,416,414,415,419,417,418,411,412,413,410,408,409,661,665,672,671,575,574,573,570,571,572,565,566,564,568,569,567,346,347,345,342,343,344,337,338,336,340,341,339,265,266,264,268,269,267,271,272,270,274,275,273,514,515,513,510,511,512,505,506,504,508,509,507,628,629,627,624,625,626,634,635,633,630,631,632,670,680,678,682,203,202,201,198,199,200,193,194,192,196,197,195,169,170,168,172,173,171,175,176,174,178,179,177,160,161,159,156,157,158,166,167,165,162,163,164,21,22,23,20,18,19,12,13,14,15,16,17,181,182,180,184,185,183,187,188,186,190,191,189,693,704,701,703,383,382,381,378,379,380,373,374,372,376,377,375,310,311,309,306,307,308,301,302,300,304,305,303,218,216,217,221,219,220,224,222,223,227,225,226,40,41,39,36,37,38,46,47,45,42,43,44,434,432,433,437,435,436,440,438,439,443,441,442,679,696,694,697,533,532,531,528,529,530,538,539,537,534,535,536,652,653,651,648,649,650,658,659,657,654,655,656,591,592,593,590,588,589,597,598,599,596,594,595,234,235,236,237,238,239,232,233,231,228,229,230,54,55,56,57,58,59,52,53,51,48,49,50,663,664,673,674,391,390,392,393,394,395,388,389,387,384,385,386,25,26,24,28,29,27,31,32,30,34,35,33,215,213,214,211,212,210,206,204,205,209,207,208,318,319,320,321,322,323,316,317,315,312,313,314,452,450,451,455,453,454,447,448,449,446,444,445,681,691,695,698,586,585,587,584,582,583,576,577,578,579,580,581,521,519,520,517,518,516,527,525,526,523,524,522,638,636,637,641,639,640,644,642,643,647,645,646,118,119,117,114,115,116,109,110,108,112,113,111,63,64,65,62,60,61,69,70,71,68,66,67,667,685,688,689,79,78,80,81,82,83,76,77,75,72,73,74,407,405,406,403,404,402,398,396,397,401,399,400,138,139,140,141,142,143,136,137,135,132,133,134,333,334,335,332,330,331,324,325,326,327,328,329,457,458,456,460,461,459,463,464,462,466,467,465,692,699,700,702,429,431,430,427,428,426,422,420,421,425,423,424,128,126,127,131,129,130,123,124,125,122,120,121,296,294,295,299,297,298,291,292,293,290,288,289,362,360,361,365,363,364,368,366,367,371,369,370,90,91,92,93,94,95,88,89,87,84,85,86,662,666,676,675,548,547,546,550,551,549,545,543,544,541,542,540,609,610,611,608,606,607,600,601,602,603,604,605,98,96,97,101,99,100,104,102,103,107,105,106,247,248,246,250,251,249,245,243,244,241,242,240,481,482,480,484,485,483,487,488,486,490,491,489,668,677,687,684 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {62} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 21:49:12 · history