Equation 677 Database

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Magma ed961bfafc8a…

magma ed961bfafc8a
Size
705
Isomorphism class hash
ed961bfafc8a0359310398c5c62e680bc7fb50c100c4566abbe7d884cbfe049d
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 16:49:51
Display reorder
660,338,87,458,362,414,459,339,415,88,363,340,413,86,460,364,341,90,410,461,365,342,91,411,462,366,343,89,412,463,367,85,336,405,456,360,337,83,406,457,361,84,335,404,455,359,81,332,408,452,356,82,333,409,453,357,80,334,407,454,358,677,680,686,675,530,157,48,494,275,49,531,276,155,495,532,277,156,50,496,533,153,274,51,497,534,154,272,52,498,535,152,273,53,499,163,528,281,46,492,529,161,282,47,493,162,527,283,45,491,159,524,280,42,488,160,525,278,43,489,158,526,279,44,490,667,664,672,670,386,284,65,470,243,63,387,244,285,471,388,242,286,64,472,389,287,246,61,473,390,288,247,62,474,391,289,245,60,475,290,384,241,56,468,385,291,239,54,469,292,383,240,55,467,293,380,237,59,464,294,381,238,57,465,295,382,236,58,466,682,676,674,678,613,144,616,614,615,624,621,623,145,622,628,631,143,632,630,637,140,639,640,638,645,141,647,648,646,653,142,655,656,654,150,597,599,600,598,604,151,607,608,606,149,589,591,592,590,146,565,564,569,568,147,572,575,576,574,148,581,583,584,582,702,697,704,703,446,94,434,422,188,435,447,189,92,423,448,190,93,436,424,449,97,191,437,425,450,95,192,438,426,451,96,193,439,427,100,444,194,432,420,445,98,195,433,421,99,443,196,431,419,103,440,197,428,416,101,441,198,429,417,102,442,199,430,418,690,691,694,692,374,259,302,178,326,303,375,327,257,176,376,328,258,304,177,377,255,329,305,181,378,256,330,306,179,379,254,331,307,180,250,372,324,300,184,373,248,325,301,182,249,371,323,299,183,253,368,320,296,187,251,369,321,297,185,252,370,322,298,186,661,662,663,666,126,41,77,74,220,78,127,218,39,75,125,219,40,79,73,122,37,223,76,72,123,38,221,561,560,124,36,222,563,562,32,117,215,17,67,118,30,216,15,68,31,116,217,16,66,35,120,214,13,70,33,121,212,14,71,34,119,213,12,69,695,696,689,693,554,231,129,482,518,130,555,519,232,483,556,520,230,128,484,557,234,521,132,485,558,235,522,133,486,559,233,523,131,487,229,552,516,135,480,553,227,517,136,481,228,551,515,134,479,225,548,512,138,476,226,549,513,139,477,224,550,514,137,478,683,684,685,687,612,3,617,618,619,625,620,627,4,626,629,635,5,633,634,636,2,643,641,642,644,1,651,649,650,652,0,659,657,658,9,596,603,601,602,605,10,611,609,610,11,588,595,593,594,8,570,571,566,567,6,573,579,577,578,7,580,587,585,586,701,699,700,698,542,269,170,350,506,171,543,507,270,351,544,508,271,172,352,545,268,509,173,353,546,266,510,174,354,547,267,511,175,355,260,540,504,168,348,541,261,505,169,349,262,539,503,167,347,263,536,500,164,344,264,537,501,165,345,265,538,502,166,346,665,669,668,671,314,107,204,398,29,205,315,27,108,399,316,28,109,203,400,317,106,25,200,401,318,104,26,201,402,319,105,24,202,403,113,312,20,210,396,313,114,18,211,397,115,311,19,209,395,112,308,23,206,392,110,309,21,207,393,111,310,22,208,394,679,681,688,673 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#3f658a46fc44ddfd8c713ec5e3bbc16ee9055426ab1786d448b9cc156d806e6f, 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 16:49:52 · history