Equation 677 Database

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Magma e3faca3364e7…

magma e3faca3364e7
Size
705
Isomorphism class hash
e3faca3364e7a88d467ea332d0b4d1c2c8333072d176aef02af9c494c5ed4b8a
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 21:56:47
Display reorder
660,412,217,536,550,119,410,215,120,534,548,411,216,121,535,549,415,213,118,539,553,413,214,116,537,551,414,212,117,538,552,208,110,531,407,545,206,111,532,408,546,207,112,533,409,547,113,211,530,406,544,114,209,528,404,542,115,210,529,405,543,684,685,676,682,512,238,332,299,376,510,239,374,333,300,511,240,375,334,298,515,241,379,335,302,513,242,377,336,303,514,243,378,337,301,236,371,338,507,297,237,372,339,508,295,235,373,340,509,296,370,232,341,506,293,368,233,342,504,294,369,234,343,505,292,671,670,667,664,251,352,564,488,462,252,350,460,562,486,250,351,461,563,487,254,355,465,567,491,255,353,463,565,489,253,354,464,566,490,347,457,559,249,483,348,458,560,247,484,349,459,561,248,485,456,346,558,245,482,454,344,556,246,480,455,345,557,244,481,687,681,674,678,629,272,631,628,633,613,273,617,615,612,621,271,625,623,620,653,268,657,655,652,637,269,641,639,636,645,270,649,647,644,278,593,591,588,589,279,601,599,596,597,277,609,607,604,605,582,274,581,585,584,478,275,0,304,219,479,276,1,305,218,703,699,704,700,161,125,187,151,181,162,126,179,185,149,163,127,180,186,150,160,124,177,183,147,158,122,178,184,148,159,123,176,182,146,131,172,193,167,157,132,170,191,168,155,133,171,192,169,156,175,130,189,166,153,173,128,190,164,154,174,129,188,165,152,692,690,689,693,364,44,259,424,524,362,45,522,260,422,363,46,523,261,423,367,47,527,258,427,365,48,525,256,425,366,49,526,257,426,42,519,265,359,419,43,520,266,360,420,41,521,267,361,421,518,38,264,358,418,516,39,262,356,416,517,40,263,357,417,661,665,663,668,23,104,438,81,36,24,105,37,439,82,25,106,35,437,80,22,107,32,434,84,20,108,33,435,85,21,109,34,436,83,102,27,429,14,79,103,28,430,15,77,101,26,428,16,78,30,98,432,17,75,31,99,433,18,76,29,100,431,19,74,695,694,696,691,474,96,400,576,450,472,97,448,398,574,473,95,449,399,575,477,92,453,403,579,475,93,451,401,577,476,94,452,402,578,87,445,395,469,571,88,446,396,470,572,86,447,397,471,573,444,90,394,468,570,442,91,392,466,568,443,89,393,467,569,675,688,679,677,635,6,634,630,632,619,7,616,618,614,627,5,624,626,622,659,2,656,658,654,643,3,640,642,638,651,4,648,650,646,12,592,594,595,590,13,600,602,603,598,11,608,610,611,606,586,8,587,583,580,441,9,540,554,318,440,10,541,555,319,701,698,702,697,328,222,314,500,282,326,220,280,312,498,327,221,281,313,499,331,225,285,317,503,329,223,283,315,501,330,224,284,316,502,228,288,309,323,495,226,286,310,324,496,227,287,311,325,497,291,231,308,322,494,289,229,306,320,492,290,230,307,321,493,662,666,669,672,388,136,61,200,66,386,134,67,59,201,387,135,65,60,202,391,139,62,57,203,389,137,63,58,204,390,138,64,56,205,142,72,52,383,198,140,73,50,384,199,141,71,51,385,197,68,145,55,382,194,69,143,53,380,195,70,144,54,381,196,683,680,673,686 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#fd86fc294900b5ccb814b44936109aa3958b6cd4f65ecf12bfe08854715a531f, 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 21:56:48 · history