Equation 677 Database

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Magma 049a6f35e42e…

magma 049a6f35e42e
Size
707
Isomorphism class hash
049a6f35e42e99a121b9edf0b4fc0d8695a4d2212777c789c74aca7f0092e9b8
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 10:31:15
Display reorder
362,361,363,364,365,360,694,49,48,50,52,53,51,158,157,156,159,160,161,166,165,167,162,163,164,267,269,268,266,264,265,71,70,69,67,68,66,273,275,274,272,270,271,17,16,15,12,13,14,278,277,276,280,281,279,47,46,45,42,43,44,171,173,172,168,169,170,155,154,153,151,152,150,428,427,429,430,431,426,349,348,350,351,352,353,526,525,527,528,524,523,393,392,394,395,390,391,449,448,444,445,446,447,442,441,443,438,439,440,432,437,433,434,435,436,563,562,564,565,596,591,593,597,592,595,594,566,631,629,652,632,650,611,612,630,616,651,608,692,691,681,675,706,684,679,705,683,322,321,323,318,320,319,113,112,111,108,109,110,23,22,21,18,20,19,105,107,106,104,102,103,327,329,328,326,325,324,90,92,91,95,93,94,75,77,76,73,74,72,252,254,253,257,255,256,232,231,233,230,228,229,244,243,245,241,242,240,239,238,237,235,236,234,598,599,601,600,538,539,486,491,487,488,489,490,409,408,410,411,412,413,514,513,510,509,511,512,497,498,499,500,501,502,505,503,506,507,508,504,553,552,554,584,585,583,571,570,568,569,521,522,532,531,533,534,535,576,607,645,648,646,622,644,660,623,659,620,617,690,704,689,670,678,665,669,672,666,61,60,62,64,65,63,218,217,216,219,220,221,175,174,176,177,178,179,247,246,248,249,250,251,259,258,260,261,262,263,183,185,184,182,180,181,314,313,312,315,316,317,96,98,97,101,99,100,299,298,297,294,295,296,137,136,135,134,132,133,119,118,117,115,116,114,358,357,359,354,355,356,368,367,369,370,371,366,403,402,404,405,406,407,483,482,484,485,480,481,544,543,545,541,540,542,385,384,386,387,388,389,550,549,551,580,581,582,573,572,574,575,529,530,558,557,559,560,561,590,633,624,621,627,647,655,615,641,649,634,658,693,696,688,667,699,685,686,677,673,121,120,122,124,125,123,282,284,283,286,287,285,138,140,139,143,141,142,300,302,301,305,303,304,7,6,8,9,10,11,190,189,191,186,187,188,56,55,54,57,58,59,205,206,204,209,207,208,212,210,211,213,214,215,5,4,3,2,1,0,227,226,225,223,224,222,605,604,602,603,536,537,401,400,396,397,398,399,470,469,471,472,473,468,372,377,373,374,375,376,516,520,515,517,518,519,464,463,465,466,467,462,547,546,548,578,579,577,588,587,589,586,555,556,495,494,496,493,492,567,628,642,640,614,656,639,625,653,606,636,613,698,697,687,668,663,671,664,695,674,24,26,25,27,28,29,41,40,39,36,37,38,79,78,83,82,81,80,87,89,88,86,85,84,202,201,203,198,199,200,30,32,31,35,33,34,289,288,290,293,291,292,310,309,311,306,307,308,128,127,126,129,130,131,149,148,147,146,144,145,197,196,195,193,194,192,420,425,421,422,423,424,337,336,338,339,340,341,347,346,342,343,344,345,455,454,450,451,452,453,382,381,383,378,379,380,334,333,335,331,330,332,476,475,477,478,479,474,460,459,461,456,457,458,419,418,414,415,416,417,619,637,657,635,618,626,643,610,638,609,654,661,662,700,682,680,676,702,701,703 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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, 5, B) with E = magma#f44078deebe7730562c927e2829a32c42b90cd1087b6200dbe445a4d4d2f9fa6, M = {108, 109, 110, 111, 112, 113, 144} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-07 10:31:16 · history