Equation 677 Database

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Magma 52aae938ebbd…

magma 52aae938ebbd
Size
705
Isomorphism class hash
52aae938ebbdd9f74fa2cd9307b70755083ee016f995aa0927beabfe561ceb0b
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 18:13:10
Display reorder
660,314,291,491,119,307,312,292,117,489,308,313,293,118,490,306,310,294,122,487,303,295,311,120,488,304,296,309,121,486,305,320,289,497,125,298,318,290,495,123,299,319,288,496,124,297,316,285,493,128,301,317,286,494,126,302,315,287,492,127,300,682,674,675,680,215,237,226,185,203,213,238,183,227,201,214,239,184,225,202,218,240,188,229,206,241,216,186,230,204,242,217,187,228,205,221,243,232,180,209,219,244,233,181,207,220,245,231,182,208,224,246,235,179,212,222,247,236,177,210,223,248,234,178,211,663,672,668,667,47,271,255,99,278,45,272,100,256,276,46,270,101,257,277,43,267,102,258,274,268,44,103,259,275,269,42,104,260,273,38,262,253,97,284,36,263,254,98,282,37,261,252,96,283,41,265,249,93,280,39,266,250,94,281,40,264,251,95,279,685,673,687,683,83,73,89,62,615,84,74,60,90,613,85,72,61,91,614,82,76,65,88,618,77,80,63,86,616,75,81,64,87,617,653,652,654,68,659,636,637,638,66,643,645,644,646,67,651,621,620,622,71,624,629,628,630,69,635,79,78,92,70,619,704,700,703,697,362,534,429,132,354,360,532,133,427,355,361,533,134,428,356,358,530,131,425,353,531,359,129,426,351,529,357,130,424,352,368,540,435,138,345,366,538,433,139,346,367,539,434,140,347,364,536,431,137,348,365,537,432,135,349,363,535,430,136,350,694,689,690,692,448,338,21,50,410,446,336,48,22,408,447,337,49,23,409,444,334,53,20,406,335,445,51,18,407,333,443,52,19,405,454,344,12,56,416,452,342,13,54,414,453,343,14,55,415,450,340,15,59,412,451,341,16,57,413,449,339,17,58,411,662,664,665,661,26,479,9,163,374,24,477,164,10,372,25,478,162,11,373,29,475,159,8,370,476,27,160,6,371,474,28,161,7,369,32,485,1,154,380,30,483,0,155,378,31,484,2,153,379,35,481,3,157,376,33,482,4,158,377,34,480,5,156,375,693,691,696,695,398,467,326,114,391,396,465,115,324,392,397,466,116,325,390,394,463,113,322,387,464,395,111,323,388,462,393,112,321,389,404,473,332,105,382,402,471,330,106,383,403,472,331,107,381,400,469,328,108,385,401,470,329,109,386,399,468,327,110,384,678,679,677,676,524,440,460,170,422,522,441,168,458,420,523,442,169,459,421,527,439,166,456,418,437,525,167,457,419,438,526,165,455,417,658,656,657,176,655,642,640,641,174,639,650,648,649,175,647,627,625,626,172,623,634,632,633,173,631,528,436,461,171,423,701,699,698,702,515,546,570,199,594,513,544,200,568,592,514,545,198,569,593,511,542,195,566,590,543,512,196,567,591,541,510,197,565,589,521,552,576,190,600,519,550,574,191,598,520,551,575,189,599,517,548,572,193,596,518,549,573,194,597,516,547,571,192,595,669,671,666,670,503,582,606,146,558,501,580,144,604,556,502,581,145,605,557,499,578,142,602,554,579,500,143,603,555,577,498,141,601,553,509,588,612,152,564,507,586,610,150,562,508,587,611,151,563,505,584,608,148,560,506,585,609,149,561,504,583,607,147,559,686,684,681,688 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#6b720d896a29843112ad3c0147d655cf7bb7a1ca51519c2978dbef59d093ebaf, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 18:13:11 · history