Equation 677 Database

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Magma 917d485b21bb…

magma 917d485b21bb
Size
381
Isomorphism class hash
917d485b21bbf4ae9f3617a18838ad6c410da391e1718b6252c448a33f7e0fbe
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:20:10
Display reorder
380,187,235,228,222,311,221,209,212,193,200,186,236,229,223,312,216,204,213,194,201,189,237,230,224,310,217,205,214,195,202,188,238,231,225,218,206,215,196,203,316,190,239,232,226,317,219,207,210,197,198,191,234,233,227,319,220,208,211,192,199,183,185,181,180,182,184,337,373,372,356,338,357,335,334,336,358,80,101,95,119,315,113,70,107,88,62,81,96,90,114,318,108,71,102,89,63,82,97,91,115,320,109,66,103,84,64,83,98,92,116,110,67,104,85,65,313,78,99,93,117,314,111,68,105,86,60,79,100,94,118,301,112,69,106,87,61,73,75,76,77,72,74,362,346,376,366,363,365,367,375,345,364,265,286,280,274,308,298,257,292,241,247,266,287,281,275,309,299,252,293,242,248,267,282,276,270,304,294,253,288,243,249,268,283,277,271,295,254,289,244,250,305,269,284,278,272,306,296,255,290,245,251,264,285,279,273,307,297,256,291,240,246,262,258,259,260,261,263,379,351,348,350,377,349,347,368,378,369,171,123,146,141,325,136,158,128,176,153,172,124,147,142,302,137,159,129,177,154,173,125,148,143,303,132,160,130,178,155,168,120,149,138,133,161,131,179,150,300,169,121,144,139,326,134,156,126,174,151,170,122,145,140,329,135,157,127,175,152,164,166,167,162,163,165,333,332,352,370,331,330,353,371,355,354,35,15,10,2,328,28,53,20,41,47,30,16,11,3,322,29,48,21,36,42,31,17,6,4,323,24,49,22,37,43,32,12,7,5,25,50,23,38,44,324,33,13,8,1,321,26,51,18,39,45,34,14,9,0,327,27,52,19,40,46,57,59,54,55,56,58,360,359,341,343,361,342,374,344,339,340 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#1c5b0e2a4c81e28721405b66c6a75a5d826a870554de2ffc705981d353b98d0b, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:20:11 · history