Equation 677 Database

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Magma 6943d4e5e56c…

magma 6943d4e5e56c
Size
705
Isomorphism class hash
6943d4e5e56c57588118e960c272542cfd73e05bb930912384c3b6e3fbccbe0a
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 18:11:28
Display reorder
660,386,509,288,437,581,582,510,387,289,438,508,580,388,287,436,577,389,505,284,433,390,578,506,285,434,579,391,507,286,435,515,384,587,294,443,385,588,295,516,444,383,586,293,514,442,583,380,290,511,439,584,381,291,512,440,585,382,292,513,441,671,669,667,662,299,37,593,232,161,159,38,300,594,230,39,160,301,592,231,164,298,36,589,235,296,162,34,590,233,163,297,35,591,234,43,305,167,599,227,306,165,600,44,228,307,166,598,45,229,170,304,595,42,226,168,302,596,40,224,169,303,597,41,225,686,690,685,689,259,605,485,569,408,409,606,257,486,570,604,407,258,484,568,404,255,601,481,565,256,405,602,482,566,406,254,603,483,567,611,250,414,491,575,248,415,492,612,576,249,413,490,610,574,410,253,487,607,571,411,251,488,608,572,412,252,489,609,573,664,672,670,668,312,179,348,187,545,546,177,313,349,188,178,544,311,347,186,541,308,182,344,183,309,542,180,345,184,543,310,181,346,185,174,318,551,354,193,319,552,355,175,194,317,550,353,176,192,547,314,350,173,189,548,315,351,171,190,549,316,352,172,191,682,683,684,674,116,336,320,197,425,426,337,114,321,195,335,424,115,322,196,421,112,332,323,200,113,422,333,324,198,423,111,334,325,199,342,122,431,326,203,120,432,327,343,201,121,430,328,341,202,427,118,329,338,206,428,119,330,339,204,429,117,331,340,205,665,663,666,661,243,497,11,402,533,534,498,244,12,403,496,532,242,10,401,529,246,493,14,398,247,530,494,15,399,531,245,495,13,400,503,241,539,17,393,239,540,18,504,394,240,538,16,502,392,535,237,20,499,396,536,238,21,500,397,537,236,19,501,395,696,695,693,697,125,420,617,46,1,634,635,123,632,633,419,0,124,616,50,3,128,416,613,47,126,4,417,614,48,2,127,418,615,49,652,131,653,654,655,129,657,658,656,659,130,649,650,648,651,637,134,638,636,639,641,132,642,640,643,645,133,646,644,647,701,703,704,702,146,9,67,207,461,462,618,144,68,619,8,460,145,66,211,457,142,5,63,208,143,458,6,64,209,459,141,7,65,210,629,137,467,73,628,135,468,74,631,630,136,466,72,626,627,463,140,69,620,621,464,138,70,623,622,465,139,71,625,624,694,700,699,698,55,449,473,276,521,522,450,56,474,277,448,520,54,472,275,517,51,445,469,272,52,518,446,470,273,519,53,447,471,274,455,61,527,479,282,62,528,480,456,283,60,526,478,454,281,523,57,475,451,278,524,58,476,452,279,525,59,477,453,280,680,677,681,678,214,31,372,154,356,357,32,212,373,155,33,358,213,371,153,359,217,30,368,157,215,360,28,369,158,361,216,29,370,156,22,220,362,378,152,218,363,379,23,150,219,364,377,24,151,365,223,374,25,148,366,221,375,26,149,367,222,376,27,147,676,679,673,675,103,75,266,90,557,558,76,104,267,91,77,556,102,268,92,553,99,78,269,89,100,554,79,270,87,555,101,80,271,88,81,109,563,264,96,110,564,265,82,97,108,562,263,83,98,559,105,260,84,95,560,106,261,85,93,561,107,262,86,94,687,691,692,688 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#6997491de262e367994a4a50c6f8055cb54c2a6a0260cea123f554e749c551e0, 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 18:11:29 · history