Equation 677 Database

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Magma a87ad5bb8c96…

magma a87ad5bb8c96
Size
705
Isomorphism class hash
a87ad5bb8c96792a4d8aa456251a226666f17aa2aa712460d6f20a0c589362d4
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 16:23:14
Display reorder
660,265,320,83,19,314,266,315,321,81,20,267,313,319,82,21,323,268,317,79,22,324,269,318,80,23,270,322,316,78,24,263,326,312,74,25,264,327,310,72,26,262,325,311,73,27,329,259,308,77,28,75,330,260,309,29,328,261,307,76,30,669,672,668,665,135,130,195,302,117,136,118,131,193,303,137,119,129,194,301,126,134,116,198,305,127,132,114,196,306,133,128,115,197,304,141,121,108,190,300,142,122,109,191,298,143,120,110,192,299,124,140,111,189,296,187,125,138,112,297,123,139,113,188,295,686,688,690,689,239,359,489,96,597,240,598,360,490,97,238,596,358,488,98,355,235,593,485,99,356,236,594,486,100,237,357,595,487,101,245,365,603,495,102,246,366,604,496,103,244,364,602,494,104,361,241,599,491,105,492,362,242,600,106,363,243,601,493,107,670,667,671,664,149,431,206,549,585,147,586,432,207,550,148,584,430,205,548,427,145,581,209,545,428,146,582,210,546,144,429,583,208,547,155,437,591,204,555,153,438,592,202,556,154,436,590,203,554,433,151,587,200,551,201,434,152,588,552,435,150,589,199,553,681,678,683,676,167,281,287,215,396,165,394,282,288,216,166,395,280,286,214,277,163,392,283,211,278,164,393,284,212,162,279,391,285,213,158,272,402,293,221,156,273,400,294,222,157,271,401,292,220,275,161,398,289,217,290,276,159,399,218,274,160,397,291,219,661,663,666,662,86,573,337,353,371,84,372,574,338,354,85,370,572,339,352,569,89,367,340,349,570,87,368,341,350,88,571,369,342,351,92,579,377,335,344,90,580,378,336,345,91,578,376,334,343,575,95,373,331,347,332,576,93,374,348,577,94,375,333,346,693,696,694,698,55,609,67,460,451,56,634,635,633,632,57,452,608,71,459,605,58,454,68,456,606,59,455,69,457,60,607,453,70,458,61,655,652,654,653,62,659,656,658,657,63,651,648,650,649,639,64,636,638,637,642,643,65,640,641,647,66,645,646,644,703,704,701,702,381,513,169,3,465,379,466,514,170,0,380,464,512,168,2,509,384,461,172,6,510,382,462,173,4,383,511,463,171,5,387,519,471,628,629,385,520,472,630,631,386,518,470,626,627,515,390,467,174,1,623,516,388,468,622,517,389,469,625,624,700,699,695,697,248,477,614,561,525,249,526,478,615,562,247,524,476,613,560,473,251,521,610,557,474,252,522,611,558,250,475,523,612,559,254,483,531,620,567,255,484,532,621,568,253,482,530,619,566,479,257,527,616,563,617,480,258,528,564,481,256,529,618,565,682,684,679,677,234,537,419,181,441,232,439,538,420,182,233,440,536,418,183,533,230,444,415,184,534,231,442,416,185,229,535,443,417,186,225,543,447,425,179,223,544,445,426,180,224,542,446,424,178,539,228,450,421,175,422,540,226,448,176,541,227,449,423,177,673,675,674,680,408,37,52,501,13,406,14,38,53,502,407,15,39,54,500,40,404,16,51,497,41,405,17,49,498,403,42,18,50,499,414,35,11,43,507,412,36,12,44,508,413,34,10,45,506,31,410,7,46,503,47,32,411,8,504,33,409,9,48,505,687,685,691,692 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#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 16:23:15 · history