Equation 677 Database

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Magma d99d14b9e61c…

magma d99d14b9e61c
Size
705
Isomorphism class hash
d99d14b9e61c23946d42b02309074afebc27e328ea9f12ed39a41c7c2b0d82c6
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 17:21:58
Display reorder
660,395,383,407,419,151,149,384,396,408,420,150,382,394,406,418,398,147,386,410,422,399,148,387,411,423,146,397,385,409,421,405,142,393,381,417,140,391,379,403,415,141,392,380,404,416,389,145,377,401,413,390,143,378,402,414,388,144,376,400,412,667,666,664,665,29,431,59,133,300,298,432,27,60,131,299,430,28,61,132,25,303,434,58,129,26,301,435,56,130,302,24,433,57,128,65,295,35,429,139,296,33,427,66,137,297,34,428,67,138,31,294,425,64,135,32,292,426,62,136,30,293,424,63,134,688,685,687,686,371,254,168,359,201,199,255,372,169,360,200,253,370,167,358,374,197,250,164,362,375,198,251,165,363,196,373,252,166,361,174,207,369,245,357,205,367,246,175,355,206,368,244,173,356,365,203,248,170,353,366,204,249,171,354,364,202,247,172,352,661,669,662,663,443,455,70,523,310,311,456,444,68,524,312,454,442,69,522,446,313,458,73,526,447,314,459,71,527,315,445,457,72,525,76,308,441,453,521,309,439,451,74,519,307,440,452,75,520,437,304,449,79,517,438,305,450,77,518,436,306,448,78,516,679,674,676,675,559,587,22,586,100,98,588,560,23,589,99,585,558,21,584,562,103,593,18,592,563,101,594,19,595,102,561,591,20,590,13,95,557,582,583,96,555,578,14,579,97,556,580,12,581,553,94,575,16,574,554,92,577,17,576,552,93,572,15,573,671,668,672,670,153,547,345,535,239,240,548,154,343,536,238,546,152,344,534,156,242,550,341,538,157,243,551,342,539,241,155,549,340,537,351,237,159,545,533,235,160,543,349,531,236,158,544,350,532,162,233,541,347,529,163,234,542,348,530,161,232,540,346,528,696,698,697,693,571,37,177,515,187,188,646,647,645,644,189,36,570,176,514,655,186,653,654,652,659,184,657,658,656,185,651,648,650,649,183,193,569,43,509,194,567,41,181,510,195,568,42,182,508,565,192,39,179,512,566,190,40,180,513,564,191,38,178,511,703,701,702,704,479,491,635,634,105,106,492,480,636,637,104,490,478,633,632,482,108,494,641,640,483,109,495,642,643,107,481,493,639,638,630,111,477,489,631,112,475,487,626,627,110,476,488,628,629,473,114,485,622,623,474,115,486,625,624,472,113,484,620,621,699,700,695,694,611,610,467,338,230,231,613,612,468,339,229,608,609,466,337,617,226,616,470,334,618,227,619,471,335,228,615,614,469,336,465,221,606,607,329,222,602,603,463,330,220,604,605,464,328,598,224,599,461,332,601,225,600,462,333,596,223,597,460,331,680,677,684,683,282,44,503,10,122,123,45,280,504,11,124,46,281,502,9,285,125,47,506,6,283,126,48,507,7,127,284,49,505,8,501,120,288,50,0,121,286,51,499,2,119,287,52,500,1,291,116,53,497,4,289,117,54,498,5,290,118,55,496,3,682,678,681,673,264,278,89,212,325,326,279,262,90,213,327,277,263,91,211,267,324,274,88,208,265,322,275,86,209,323,266,276,87,210,80,316,259,269,218,317,260,270,81,219,318,261,268,82,217,258,319,272,83,214,256,320,273,84,215,257,321,271,85,216,689,690,692,691 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#4f5c530836fd0cc12915654d9cb933b30b1ebf0f1cb96882ec953efd42c5ac65, 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 17:21:59 · history