Equation 677 Database

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Magma 83a505c76106…

magma 83a505c76106
Size
705
Isomorphism class hash
83a505c7610670bbb25b78a6270926e8927722b97d6d7706fa790514bbb30e20
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 16:22:56
Display reorder
660,37,270,163,460,544,38,545,271,164,461,36,543,272,162,459,273,40,540,166,456,274,41,541,167,457,39,275,542,165,458,43,276,550,169,466,44,277,551,170,467,42,278,549,168,465,279,46,546,172,462,173,280,47,547,463,281,45,548,171,464,678,679,682,686,311,110,472,83,436,309,437,108,473,81,310,435,109,471,82,113,307,432,468,79,111,308,433,469,80,306,112,434,470,78,317,105,442,478,89,315,106,443,479,87,316,107,441,477,88,104,313,438,474,85,475,102,314,439,86,103,312,440,476,84,662,666,664,671,91,329,56,562,424,92,425,327,54,563,90,423,328,55,561,325,94,420,59,558,326,95,421,57,559,93,324,422,58,560,97,320,430,51,568,98,318,431,52,569,96,319,429,53,567,323,100,426,50,564,48,321,101,427,565,322,99,428,49,566,684,680,676,673,126,344,556,75,418,127,419,342,557,76,128,417,343,555,77,347,129,414,552,74,345,130,415,553,72,131,346,416,554,73,132,645,649,650,644,133,652,657,658,653,134,637,641,642,636,612,135,615,617,616,626,622,136,625,620,630,137,633,634,628,703,701,704,698,177,532,484,160,448,178,449,533,485,161,179,447,531,483,159,528,176,444,480,156,529,174,445,481,157,175,530,446,482,158,183,538,454,490,151,184,539,455,491,152,185,537,453,489,150,534,182,450,486,154,487,535,180,451,155,536,181,452,488,153,689,692,691,694,114,406,331,4,253,115,254,407,332,5,116,252,405,330,3,402,117,256,334,1,403,118,257,335,0,119,404,255,333,2,120,412,251,337,10,121,413,249,338,11,122,411,250,336,9,408,123,247,340,6,341,409,124,248,7,410,125,246,339,8,661,665,667,663,60,385,520,218,225,61,226,386,521,216,62,227,384,519,217,388,63,224,516,221,389,64,222,517,219,65,387,223,518,220,66,383,231,526,213,67,381,232,527,214,68,382,233,525,215,379,69,230,522,212,523,380,70,228,210,378,71,229,524,211,695,693,696,690,244,586,604,394,370,245,371,587,605,395,243,369,585,603,393,582,240,366,600,390,583,241,367,601,391,242,584,368,602,392,235,592,376,610,400,236,593,377,611,401,234,591,375,609,399,588,238,372,606,396,607,589,239,373,397,590,237,374,608,398,675,688,674,685,18,363,350,358,598,19,599,364,348,359,20,597,365,349,357,362,21,594,353,354,360,22,595,351,355,23,361,596,352,356,16,648,651,646,647,17,656,659,654,655,15,640,643,638,639,618,12,619,613,614,621,624,13,627,623,632,14,635,629,631,697,700,702,699,147,292,297,574,496,148,497,293,298,575,149,495,291,299,573,288,146,492,296,570,289,144,493,294,571,145,290,494,295,572,138,283,502,303,580,139,284,503,304,581,140,282,501,305,579,286,141,498,302,576,300,287,142,499,577,285,143,500,301,578,670,672,668,669,25,266,192,208,508,26,509,264,193,209,24,507,265,194,207,269,28,504,195,204,267,29,505,196,205,27,268,506,197,206,31,261,514,190,199,32,262,515,191,200,30,263,513,189,198,260,34,510,186,202,187,258,35,511,203,259,33,512,188,201,683,687,681,677 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#2ec821928dae411f986b7c636eee0f3d0451d16a0e775a52641e8351195889f9, 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 16:22:57 · history