Equation 677 Database

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Magma 7a63c73d71d1…

magma 7a63c73d71d1
Size
595
Isomorphism class hash
7a63c73d71d15447e3a0b1443da017f5079db5c9bf6a2a4c03be306be1efd82c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 10:31:25
Display reorder
120,115,116,117,118,119,56,55,51,52,53,54,125,124,126,127,128,123,385,384,383,388,386,387,314,316,315,311,312,313,534,535,576,558,574,275,274,174,276,277,219,195,74,75,76,77,73,107,106,108,103,104,105,49,48,50,237,238,47,242,241,199,200,121,122,136,135,137,138,139,245,211,258,212,259,209,210,234,192,235,190,236,191,193,57,58,59,60,61,507,509,508,504,505,506,308,310,309,307,305,306,333,332,334,331,329,330,405,404,406,402,403,401,297,296,298,294,295,293,442,441,440,437,438,439,339,338,340,337,335,336,522,546,520,525,524,512,510,593,570,555,580,577,563,588,569,559,9,8,10,11,12,13,72,71,67,68,69,70,32,31,27,28,29,30,84,89,85,86,87,88,44,43,45,46,41,42,160,159,161,162,163,249,246,152,247,248,202,201,261,227,34,260,228,182,194,66,62,63,64,65,320,322,321,317,318,319,477,476,478,473,474,475,501,503,502,498,500,499,417,416,418,414,415,413,457,456,455,460,458,459,368,370,369,366,367,365,429,428,430,427,425,426,527,526,528,523,518,519,545,548,556,568,584,560,562,547,551,561,153,158,154,155,156,157,141,140,142,143,144,145,35,40,36,37,38,39,80,79,81,82,83,78,109,114,110,111,112,113,3,2,4,0,1,280,286,175,287,283,278,279,281,284,129,285,282,243,244,131,132,133,134,130,412,411,410,409,407,408,399,398,400,395,396,397,350,352,351,348,349,347,342,341,343,345,346,344,485,288,289,292,290,291,357,356,358,355,353,354,433,432,431,434,435,436,538,531,515,521,514,511,516,583,557,564,575,571,581,594,578,579,20,25,21,22,23,24,168,267,215,265,216,266,208,207,252,205,253,206,240,198,197,94,95,96,171,170,172,173,271,272,164,251,273,203,204,250,186,230,183,229,184,185,232,188,233,189,231,187,181,225,226,33,223,224,486,487,488,490,491,489,451,450,449,453,454,452,363,362,364,361,359,360,447,446,448,444,445,443,391,390,389,394,392,393,327,326,328,325,323,324,423,422,424,421,419,420,540,544,533,536,513,537,532,549,586,567,585,592,590,582,552,554,150,149,151,146,147,148,166,256,257,165,254,255,213,214,262,263,167,264,220,176,177,6,7,5,91,90,92,93,196,239,221,222,178,179,180,26,15,14,16,17,18,19,99,98,100,101,102,97,169,218,269,270,268,217,480,479,481,483,484,482,376,375,374,372,373,371,495,497,496,493,494,492,462,461,463,465,466,464,472,471,470,469,467,468,303,302,304,301,299,300,377,379,378,381,382,380,530,529,542,517,541,539,543,572,589,553,550,566,587,565,573,591 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#5d364ad3474cdcd7c6d5defafd2fd9bfd394ea971d15e95ed0d16a1c5a75c76d, M = the submagma generated by {0, 18} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 10:31:26 · history