Equation 677 Database

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Magma 8cd1f376e330…

magma 8cd1f376e330
Size
705
Isomorphism class hash
8cd1f376e3301b03d6ef4d59b9de9f45c3576f9d264d450d53a6e87ac55f9b3b
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 17:44:46
Display reorder
660,287,566,362,522,494,288,567,363,523,495,286,565,361,521,493,562,290,358,518,490,563,291,359,519,491,564,289,360,520,492,285,557,353,513,485,283,558,354,514,486,284,556,352,512,484,560,281,356,516,488,561,282,357,517,489,559,280,355,515,487,684,682,687,676,146,253,227,237,242,147,254,225,238,240,145,252,226,239,241,256,149,223,236,245,257,150,224,234,243,255,148,222,235,244,152,259,218,228,248,153,260,216,229,246,151,258,217,230,247,262,155,221,231,251,263,156,219,232,249,261,154,220,233,250,672,662,666,664,69,398,470,374,302,67,399,471,375,303,68,397,469,373,301,394,72,466,370,298,395,70,467,371,299,396,71,468,372,300,64,389,461,365,293,65,390,462,366,294,66,388,460,364,292,392,63,464,368,296,393,61,465,369,297,391,62,463,367,295,677,673,678,681,43,647,651,644,649,45,655,659,653,657,47,639,643,636,641,615,42,619,612,617,623,38,627,621,625,631,39,635,629,633,56,266,569,211,525,58,267,570,209,526,59,265,568,210,524,598,53,599,600,601,607,50,611,605,609,264,52,571,1,527,703,699,704,701,170,91,108,304,410,171,92,106,305,411,169,93,107,306,409,94,173,104,307,406,95,174,105,308,407,96,172,103,309,408,176,89,99,310,401,177,90,97,311,402,175,88,98,312,400,85,179,102,313,404,86,180,100,314,405,87,178,101,315,403,694,690,689,693,55,331,30,482,386,57,332,31,483,387,60,333,29,481,385,330,54,26,478,382,328,49,27,479,383,329,51,28,480,384,13,337,36,473,377,40,338,37,474,378,41,339,35,472,376,336,44,32,476,380,334,46,33,477,381,335,48,34,475,379,665,663,661,669,112,181,196,8,422,113,182,197,9,423,114,183,198,7,421,184,111,195,11,418,185,109,193,12,419,186,110,194,10,420,118,187,202,6,413,119,188,203,4,414,120,189,204,5,412,190,117,201,2,416,191,115,199,3,417,192,116,200,0,415,695,691,696,692,74,446,510,434,594,75,447,511,435,595,73,445,509,433,593,442,77,506,430,590,443,78,507,431,591,444,76,508,432,592,80,437,501,425,585,81,438,502,426,586,79,436,500,424,584,440,83,504,428,588,441,84,505,429,589,439,82,503,427,587,679,688,680,683,129,650,648,646,645,127,658,656,654,652,128,642,640,638,637,618,132,616,614,613,626,130,624,622,620,634,131,632,630,628,124,554,499,208,214,125,552,497,206,212,126,553,498,207,213,603,123,602,597,596,610,121,608,604,606,555,122,496,205,215,700,698,702,697,133,549,548,161,582,134,551,550,162,583,135,546,547,160,581,541,136,540,157,578,543,137,542,158,579,545,138,544,159,580,139,531,530,167,573,140,533,532,168,574,141,528,529,166,572,537,142,536,163,576,539,143,538,164,577,534,144,535,165,575,670,671,668,667,22,325,271,458,341,20,326,272,459,342,21,327,273,457,340,324,25,270,454,344,322,23,268,455,345,323,24,269,456,343,17,316,277,449,347,18,317,278,450,348,19,318,279,448,346,319,16,276,452,350,320,14,274,453,351,321,15,275,451,349,686,675,685,674 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#61e4460e7132ae46985bdc51b44ba41f1d8967bba1a2e054d2c046422600ec54, 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 17:44:48 · history