Equation 677 Database

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Magma 4f98079dd139…

magma 4f98079dd139
Size
705
Isomorphism class hash
4f98079dd139642612546b7d52a462ec12a80ca08104ae386ed1af06f1a0baf9
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 15:54:40
Display reorder
660,642,640,51,643,650,52,602,603,610,601,53,622,621,623,630,50,562,560,563,570,48,582,580,583,590,542,49,541,543,550,57,462,460,463,470,423,422,424,58,429,440,442,443,59,450,521,522,523,56,530,480,482,483,54,490,500,502,503,55,510,690,696,693,694,644,653,130,649,652,131,604,609,612,613,129,624,633,629,632,126,564,573,569,572,127,584,593,589,592,544,128,553,549,552,121,464,473,469,472,425,432,428,122,431,453,444,449,120,452,533,524,529,124,532,493,484,489,125,492,513,504,509,123,512,703,692,699,695,371,208,36,286,137,37,369,287,135,209,38,370,207,285,136,39,367,204,282,133,40,368,205,283,134,366,41,206,284,132,42,362,214,277,143,360,215,278,43,141,213,361,276,44,142,210,365,280,45,139,211,363,281,46,140,212,364,279,47,138,676,666,669,673,160,323,14,180,419,12,161,181,417,321,13,159,322,182,418,17,156,319,183,415,15,157,320,184,416,158,16,318,185,414,20,166,314,186,410,167,312,187,18,408,313,165,188,19,409,317,162,189,23,413,315,163,190,21,411,316,164,191,22,412,668,678,680,664,645,654,260,648,646,258,605,608,606,614,259,625,634,628,626,263,565,574,568,566,261,585,594,588,586,545,262,554,548,546,255,465,474,468,466,426,439,438,256,437,454,445,448,257,446,534,525,528,254,526,494,485,488,252,486,514,505,508,253,506,697,687,688,701,659,641,61,658,656,62,619,618,616,600,60,639,620,638,636,64,579,561,578,576,65,599,581,598,596,559,63,540,558,556,67,479,461,478,476,420,421,436,68,434,441,459,458,66,456,520,539,538,70,536,481,499,498,71,496,501,519,518,69,516,704,700,689,686,651,657,32,647,655,30,611,607,615,617,31,631,637,627,635,35,571,577,567,575,33,591,597,587,595,551,34,557,547,555,27,471,477,467,475,430,435,427,28,433,457,451,447,29,455,537,531,527,26,535,497,491,487,24,495,517,511,507,25,515,685,698,691,702,192,218,145,311,347,146,193,309,345,216,144,194,217,310,346,148,195,221,307,343,149,196,219,308,344,197,147,220,306,342,151,198,224,302,338,199,222,300,152,336,223,200,301,150,337,227,201,305,154,341,225,202,303,155,339,226,203,304,153,340,663,667,681,683,335,76,3,359,169,4,333,357,170,77,5,334,75,358,168,2,331,72,355,172,1,332,73,356,173,330,0,74,354,171,9,326,82,350,175,324,83,348,10,176,81,325,349,11,174,78,329,353,8,178,79,327,351,6,179,80,328,352,7,177,684,674,665,671,115,299,98,395,383,96,116,393,381,297,97,114,298,394,382,101,118,295,391,379,99,119,296,392,380,117,100,294,390,378,104,113,290,386,374,111,288,384,102,372,289,112,385,103,373,293,109,389,107,377,291,110,387,105,375,292,108,388,106,376,672,670,662,661,269,407,84,245,229,85,267,243,230,405,86,268,406,244,228,87,265,403,241,232,88,266,404,242,233,264,89,402,240,231,90,275,398,251,235,273,396,249,91,236,397,274,250,92,234,401,271,247,93,238,399,272,248,94,239,400,270,246,95,237,679,682,677,675 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#24594adec9458e953c3b7e97dafa6bb51a67ac64efb5ebe0d91d39b768cf806c, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 15:54:41 · history