Equation 677 Database

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Magma 11ee3122c12b…

magma 11ee3122c12b
Size
381
Isomorphism class hash
11ee3122c12baf4f2c4a744a295984d00931332b9a5314e6baa6bfb24ffa185c
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 23:48:21
Display reorder
380,116,111,121,7,8,285,196,200,191,180,185,175,4,275,3,75,80,70,216,205,210,231,220,225,314,312,313,317,315,316,97,85,90,105,101,280,137,126,131,146,141,290,237,242,247,252,257,262,151,155,160,166,171,295,270,61,66,46,51,56,30,42,37,265,21,26,335,364,340,365,345,350,355,375,332,371,117,112,122,10,11,287,195,201,190,181,186,176,6,277,5,77,82,72,215,206,211,230,221,226,306,307,308,309,310,311,95,87,92,107,102,282,136,127,130,145,140,291,235,240,245,250,256,261,150,156,161,165,170,296,272,62,67,47,52,57,31,41,36,267,22,27,337,361,342,366,347,352,357,376,330,373,119,114,124,16,17,289,199,204,194,184,189,179,19,279,18,79,84,74,219,209,214,234,224,229,324,325,326,327,328,329,99,89,94,109,104,284,139,129,134,149,144,294,239,244,249,254,259,264,154,159,164,169,174,299,274,64,69,49,54,59,33,44,39,269,24,29,339,363,344,369,349,354,359,379,334,374,115,110,120,9,1,286,197,202,192,182,187,177,0,276,2,76,81,71,217,207,212,232,222,227,301,300,302,303,304,305,96,86,91,106,100,281,135,125,132,147,142,292,236,241,246,251,255,260,152,157,162,167,172,297,271,60,65,45,50,55,34,40,35,266,20,25,336,360,341,367,346,351,356,377,331,370,118,113,123,14,15,288,198,203,193,183,188,178,12,278,13,78,83,73,218,208,213,233,223,228,319,320,318,322,323,321,98,88,93,108,103,283,138,128,133,148,143,293,238,243,248,253,258,263,153,158,163,168,173,298,273,63,68,48,53,58,32,43,38,268,23,28,338,362,343,368,348,353,358,378,333,372 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#e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76, M = {74} 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 23:48:22 · history