Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma a7252a1bc14d…

magma a7252a1bc14d
Size
705
Isomorphism class hash
a7252a1bc14dfed0f91897b0b1787a4906a2b692fc3195c36a17bd139753558f
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 21:46:57
Display reorder
660,44,347,289,394,50,45,345,290,392,51,46,346,291,393,52,350,43,288,397,49,348,286,395,47,41,349,42,287,396,48,35,295,353,400,56,36,296,351,398,57,37,297,352,399,58,294,38,356,403,55,401,292,39,354,53,293,40,355,402,54,675,676,674,673,73,249,212,237,225,71,247,213,235,223,72,248,211,236,224,245,76,208,233,221,246,209,234,222,74,244,75,210,232,220,79,203,240,228,216,77,204,238,226,214,78,202,239,227,215,206,82,243,231,219,229,207,80,241,217,205,81,242,230,218,668,670,672,661,94,486,440,534,253,92,484,438,532,254,93,485,439,533,255,489,90,443,537,252,487,441,535,250,91,488,89,442,536,251,85,446,492,540,259,83,444,490,538,260,84,445,491,539,261,449,88,495,543,258,541,447,86,493,256,448,87,494,542,257,682,683,678,680,134,406,383,475,6,135,404,381,473,7,136,405,382,474,5,409,133,386,478,9,407,384,476,10,131,408,132,385,477,8,140,389,412,481,4,141,387,410,479,2,142,388,411,480,3,652,139,654,657,656,482,390,137,413,0,391,138,414,483,1,704,702,703,699,120,498,299,546,183,121,496,300,544,181,119,497,298,545,182,501,123,302,549,179,499,303,547,180,124,500,122,301,548,178,126,305,504,552,189,127,306,502,550,187,125,304,503,551,188,308,129,507,555,185,553,309,130,505,186,307,128,506,554,184,694,693,689,691,98,265,522,369,362,99,266,520,370,360,100,267,521,371,361,264,97,525,372,358,262,523,373,359,95,263,96,524,374,357,104,528,271,375,368,105,526,272,376,366,106,527,273,377,367,531,103,270,378,364,379,529,101,268,365,530,102,269,380,363,664,663,665,666,323,155,11,194,510,324,156,12,195,508,322,157,13,193,509,158,326,14,190,513,159,15,191,511,327,160,325,16,192,512,329,17,161,200,516,330,18,162,201,514,328,19,163,199,515,20,332,164,196,519,197,21,333,165,517,22,331,166,198,518,695,692,696,690,112,417,570,606,642,110,415,568,604,640,111,416,569,605,641,420,108,573,609,645,418,571,607,643,109,419,107,572,608,644,118,576,423,612,648,116,574,421,610,646,117,575,422,611,647,579,114,426,615,651,613,577,115,424,649,578,113,425,614,650,686,688,684,677,30,429,172,464,344,31,427,173,462,342,29,428,174,463,343,432,33,175,467,340,430,176,465,341,34,431,32,177,466,339,28,170,435,470,338,26,171,433,468,336,27,169,434,469,337,658,24,659,655,653,471,167,25,436,335,168,23,437,472,334,701,697,698,700,64,558,594,452,630,62,556,592,450,628,63,557,593,451,629,561,60,597,455,633,559,595,453,631,61,560,59,596,454,632,70,600,564,458,636,68,598,562,456,634,69,599,563,457,635,603,66,567,461,639,459,601,67,565,637,602,65,566,460,638,662,671,669,667,145,618,321,274,582,143,616,319,275,580,144,617,320,276,581,621,148,317,277,585,619,318,278,583,146,620,147,316,279,584,151,312,624,280,588,149,310,622,281,586,150,311,623,282,587,315,154,627,283,591,284,313,152,625,589,314,153,626,285,590,681,685,679,687 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#f4f724834d898f30c0a6fbb58eb0b496232f556dc00d71550d6e526db5e670b8, 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 21:46:58 · history