Equation 677 Database

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Magma cf3ea297316e…

magma cf3ea297316e
Size
705
Isomorphism class hash
cf3ea297316e6b5c23dd8217504eaecba8267437681ca69d23f86cc5aa233ec4
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 17:41:36
Display reorder
660,64,128,422,446,189,65,129,423,447,187,66,424,448,188,127,131,63,421,445,192,132,61,419,443,190,130,62,420,444,191,134,413,55,437,195,135,414,56,438,193,133,415,57,439,194,416,137,58,440,198,417,138,59,441,196,418,136,60,442,197,665,664,669,672,42,296,386,293,434,40,297,387,294,435,41,388,292,436,295,299,38,385,289,433,300,39,383,290,431,298,37,384,291,432,302,377,33,284,425,303,378,31,285,426,301,379,32,283,427,380,305,36,287,428,381,306,34,288,429,382,304,35,286,430,690,686,687,685,162,565,589,529,217,160,566,590,530,218,161,591,531,219,567,564,158,588,528,220,562,159,586,526,221,563,157,587,527,222,556,580,153,520,215,557,581,151,521,216,558,582,152,522,214,583,559,156,523,211,584,560,154,524,212,585,561,155,525,213,667,670,662,668,98,307,330,398,342,99,308,328,399,340,97,329,400,341,309,310,101,326,397,338,311,102,327,395,339,312,100,325,396,337,313,321,96,389,333,314,319,94,390,331,315,320,95,391,332,324,316,92,392,336,322,317,93,393,334,323,318,91,394,335,675,678,680,682,111,410,505,623,354,109,411,506,624,352,110,507,625,353,412,409,114,504,622,350,407,112,502,620,351,408,113,503,621,349,401,496,106,614,345,402,497,107,615,343,403,498,108,616,344,499,404,105,617,348,500,405,103,618,346,501,406,104,619,347,671,666,661,663,146,207,458,541,493,147,205,459,542,494,145,460,543,495,206,210,149,457,540,492,208,150,455,538,490,209,148,456,539,491,202,449,144,532,484,203,450,142,533,485,204,451,143,534,486,452,201,140,535,487,453,199,141,536,488,454,200,139,537,489,697,694,696,693,12,647,479,1,483,10,655,654,653,652,11,656,658,657,659,646,15,480,3,29,644,13,481,0,30,645,14,482,2,28,638,477,18,7,24,639,478,16,8,22,640,476,17,9,23,473,641,21,6,27,474,642,19,4,25,475,643,20,5,26,703,701,702,704,77,81,610,355,470,78,79,648,649,471,76,650,651,472,80,84,73,611,356,469,82,74,612,357,467,83,75,613,358,468,87,608,68,363,461,85,609,69,364,462,86,607,67,362,463,604,90,71,359,464,605,88,72,360,465,606,89,70,361,466,699,700,695,698,116,185,601,577,272,117,186,602,578,273,115,603,579,271,184,181,119,600,576,275,182,120,598,574,276,183,118,599,575,274,176,592,122,568,278,177,593,123,569,279,175,594,121,570,277,595,179,125,571,281,596,180,126,572,282,597,178,124,573,280,679,681,673,684,49,517,635,553,374,50,518,636,554,375,51,637,555,376,519,516,52,634,552,373,514,53,632,550,371,515,54,633,551,372,508,626,47,544,365,509,627,48,545,366,510,628,46,546,367,629,511,43,547,368,630,512,44,548,369,631,513,45,549,370,677,683,674,676,171,237,257,226,259,169,235,258,227,260,170,256,228,261,236,240,174,253,225,262,238,172,254,223,263,239,173,255,224,264,243,248,166,232,265,241,249,167,233,266,242,247,168,234,267,251,246,165,231,268,252,244,163,229,269,250,245,164,230,270,689,688,692,691 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#5e8db79a467cc4283015956475779111852195ee797ae26ed1a0610c426b851f, 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 17:41:38 · history