Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 8c1ff8f08e88…

magma 8c1ff8f08e88
Size
705
Isomorphism class hash
8c1ff8f08e8870b67b5cb361881e2a9aef379f26ec35f315877648ee9704e17b
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 16:24:07
Display reorder
660,450,235,522,498,402,451,236,523,499,403,452,234,524,500,404,453,238,525,501,405,239,454,526,502,406,503,455,237,527,407,520,448,233,496,400,521,449,231,497,401,519,447,232,495,399,444,516,229,492,396,445,517,230,493,397,446,518,228,494,398,684,677,686,680,167,80,426,145,139,165,78,427,146,140,166,79,428,144,138,163,83,429,148,142,81,164,430,149,143,147,162,82,431,141,424,158,75,151,137,425,156,76,152,135,423,157,77,150,136,161,420,74,154,133,159,421,72,155,134,160,422,73,153,132,671,668,665,663,474,177,93,546,17,475,178,94,547,15,476,179,95,548,16,477,176,92,549,13,174,478,90,550,14,551,479,175,91,12,84,472,168,544,23,85,473,169,545,21,86,471,170,543,22,468,87,171,540,19,469,88,172,541,20,470,89,173,542,18,687,683,679,681,614,52,616,617,612,622,53,624,625,620,630,51,632,633,628,638,48,640,641,636,49,646,648,649,645,657,654,50,656,653,600,598,58,601,597,608,606,59,609,604,592,590,57,593,589,565,566,54,569,568,575,576,55,577,572,583,584,56,585,580,703,700,702,704,290,240,378,276,366,288,241,379,277,367,289,242,380,278,368,293,243,381,279,369,244,291,382,280,370,281,292,245,383,371,376,296,246,282,364,377,294,247,283,365,375,295,248,284,363,299,372,249,285,360,297,373,250,286,361,298,374,251,287,362,694,691,692,689,414,184,510,462,438,415,185,511,463,439,416,183,512,464,440,417,180,513,465,441,181,418,514,466,442,467,419,182,515,443,508,412,190,460,436,509,413,191,461,437,507,411,189,459,435,408,504,186,456,432,409,505,187,457,433,410,506,188,458,434,667,666,669,664,318,269,340,6,215,319,267,341,7,213,320,268,339,8,214,321,265,336,9,211,266,322,337,10,212,11,323,264,338,210,346,316,275,4,206,347,317,273,5,204,345,315,274,3,205,312,342,271,1,209,313,343,272,0,207,314,344,270,2,208,693,695,696,690,217,37,66,486,558,218,38,67,487,559,216,36,68,488,560,220,40,69,489,561,41,221,70,490,562,491,219,39,71,563,64,223,43,484,556,65,224,44,485,557,63,222,42,483,555,226,60,46,480,552,227,61,47,481,553,225,62,45,482,554,682,688,676,678,613,192,618,619,615,621,193,626,627,623,629,194,634,635,631,637,195,642,643,639,196,644,650,651,647,659,652,197,658,655,602,596,198,603,599,610,605,199,611,607,594,588,200,595,591,570,571,201,567,564,573,578,202,579,574,581,586,203,587,582,699,701,697,698,112,107,131,534,354,113,105,129,535,355,111,106,130,536,356,108,103,127,537,357,104,109,128,538,358,539,110,102,126,359,122,118,98,532,352,120,119,96,533,353,121,117,97,531,351,114,125,101,528,348,115,123,99,529,349,116,124,100,530,350,672,662,661,670,304,262,330,390,28,305,263,331,391,29,303,261,332,392,27,300,258,333,393,24,259,301,334,394,25,395,302,260,335,26,328,310,253,388,34,329,311,254,389,35,327,309,252,387,33,306,324,256,384,30,307,325,257,385,31,308,326,255,386,32,675,685,673,674 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#2fbfbc696f8770de67b632f9354275e3bbc4952318d0e644426634c23ae4ab08, 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 16:24:08 · history