Equation 677 Database

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Magma 4d618ed76098…

magma 4d618ed76098
Size
396
Isomorphism class hash
4d618ed760988eed77a9529cb223a74b23ef00c6277ad8ae9c419be257ba5efd
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 06:06:16
Display reorder
395,367,319,350,325,108,316,22,103,109,74,23,104,110,75,24,105,111,76,25,106,112,77,306,326,328,317,307,95,113,78,16,96,114,79,17,97,115,80,18,98,116,81,19,99,117,82,20,100,329,318,308,324,327,83,21,101,102,84,107,15,92,94,85,86,87,88,89,90,91,320,93,321,322,323,357,385,390,383,388,315,48,246,239,72,49,247,240,73,50,248,241,63,51,249,242,64,41,250,243,65,42,251,363,356,310,252,233,66,43,253,234,67,40,344,342,352,366,345,343,314,44,254,235,68,45,255,236,69,311,364,362,70,46,244,237,238,47,71,245,31,37,38,39,26,27,28,29,30,32,33,34,35,36,309,376,382,393,387,373,354,358,127,281,5,133,128,282,6,134,129,283,7,135,130,280,8,136,131,287,9,137,132,288,10,138,118,290,11,139,119,292,12,140,120,294,13,141,121,296,14,142,122,298,2,143,123,300,3,144,124,302,4,145,125,126,1,304,146,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,394,379,378,380,355,338,347,219,54,200,266,220,55,201,267,221,56,202,256,222,313,339,365,223,57,203,257,224,58,204,258,225,59,205,259,226,60,206,260,227,351,368,346,228,61,196,261,229,62,197,262,230,52,198,263,231,53,199,264,232,361,337,312,265,218,210,211,212,213,214,215,216,217,207,208,209,340,341,360,384,377,391,386,372,332,353,183,268,170,152,184,269,171,153,185,270,159,154,186,271,160,155,187,272,161,156,188,273,162,157,189,274,163,158,190,275,164,330,335,348,359,331,336,349,165,147,191,276,166,148,192,277,167,149,193,278,168,150,194,195,169,279,151,0,173,174,175,176,177,178,179,180,181,182,172,333,334,371,375,389,381,392 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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#9916b9303e5777c051d457f13e65b220048127e3f9475b765d37bfd24fd4df83, M = {75} 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, 79): MacNeish's product over GF(79); 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: 21.

last edited by qawbecrdtey at 2026-10-02 06:06:18 · history