Equation 677 Database

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Magma 5b520146a0da…

magma 5b520146a0da
Size
705
Isomorphism class hash
5b520146a0da601012eacde74f8d7938567004e25e725075c129b017c1aad02c
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 19:19:49
Display reorder
660,228,203,104,495,471,229,472,204,105,496,227,473,205,103,497,224,202,470,100,494,225,200,468,101,492,226,201,469,102,493,234,209,477,110,501,235,210,478,111,502,233,211,479,109,503,208,230,476,106,500,206,231,474,107,498,207,232,475,108,499,684,679,685,678,147,351,97,359,383,148,384,352,98,360,149,385,350,99,361,146,354,382,96,358,144,355,380,94,356,145,353,381,95,357,153,349,389,88,365,154,347,390,89,366,155,348,391,90,367,345,152,388,91,364,346,150,386,92,362,344,151,387,93,363,667,663,662,664,238,515,13,156,371,236,372,516,14,157,237,373,517,12,158,241,514,370,16,159,239,512,368,17,160,240,513,369,15,161,244,521,377,19,162,242,522,378,20,163,243,523,379,18,164,520,247,376,22,165,518,245,374,23,166,519,246,375,21,167,682,674,680,675,119,407,127,427,507,120,508,408,128,428,118,509,409,129,429,122,406,506,126,426,123,404,504,124,424,121,405,505,125,425,117,640,642,638,641,115,648,650,646,649,116,656,658,654,657,630,113,631,632,633,410,114,510,130,430,411,112,511,131,431,703,697,704,700,38,483,212,459,587,36,588,484,213,460,37,589,485,214,461,41,482,586,215,458,39,480,584,216,456,40,481,585,217,457,44,489,593,218,465,42,490,594,219,466,43,491,595,220,467,488,47,592,221,464,486,45,590,222,462,487,46,591,223,463,689,692,693,694,173,290,551,415,395,171,396,291,552,416,172,397,292,553,417,169,293,394,550,414,170,294,392,548,412,168,295,393,549,413,179,288,401,557,421,177,289,402,558,422,178,287,403,559,423,284,175,400,556,420,285,176,398,554,418,286,174,399,555,419,670,665,661,672,51,324,273,261,314,52,315,325,274,262,53,316,323,272,260,50,320,317,276,264,48,321,318,277,265,49,322,319,275,263,57,330,312,279,267,58,331,313,280,268,59,329,311,278,266,326,56,308,282,270,327,54,309,283,271,328,55,310,281,269,695,690,696,691,254,191,447,619,335,255,336,192,448,620,256,337,193,449,621,257,190,334,446,618,258,188,332,444,616,259,189,333,445,617,252,197,341,453,625,253,198,342,454,626,251,199,343,455,627,196,248,340,452,624,194,249,338,450,622,195,250,339,451,623,676,688,677,673,66,611,83,75,187,67,185,612,84,76,68,186,613,85,77,69,610,183,82,74,70,608,184,80,72,71,609,182,81,73,64,643,639,636,637,65,651,647,644,645,63,659,655,652,653,635,60,634,628,629,614,61,181,86,78,615,62,180,87,79,701,698,702,699,142,435,28,539,563,143,564,436,29,540,141,565,437,27,541,138,434,562,24,538,139,432,560,25,536,140,433,561,26,537,133,441,569,34,545,134,442,570,35,546,132,443,571,33,547,440,136,568,30,544,438,137,566,31,542,439,135,567,32,543,668,669,666,671,3,575,527,599,305,4,306,576,528,600,5,307,577,529,601,2,574,304,526,598,1,572,302,524,596,0,573,303,525,597,9,581,296,533,605,10,582,297,534,606,11,583,298,535,607,580,8,299,532,604,578,6,300,530,602,579,7,301,531,603,681,686,683,687 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#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 19:19:50 · history