Equation 677 Database

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Magma dad742b49738…

magma dad742b49738
Size
381
Isomorphism class hash
dad742b49738d31518ac271222c02f117581b52a716ecf6bc141b584d1a28943
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 23:15:56
Display reorder
380,30,26,271,35,41,46,206,211,216,220,225,230,247,237,242,262,252,257,186,176,181,200,190,195,71,275,66,57,60,52,291,145,140,131,135,126,20,265,15,7,12,2,170,295,166,155,160,150,86,91,96,75,281,80,327,329,324,326,325,328,110,106,101,286,120,115,351,356,365,370,337,361,345,341,332,375,31,25,270,36,40,45,205,210,215,221,226,231,245,236,241,261,251,256,185,175,180,201,191,196,70,276,65,58,61,53,290,146,141,130,136,125,22,266,19,5,10,0,171,296,165,156,161,151,85,90,95,76,280,81,306,308,309,311,310,307,111,105,100,285,121,116,350,355,366,371,335,360,346,340,331,376,32,27,272,37,42,47,207,212,217,222,227,232,246,235,240,260,250,255,187,177,182,202,192,197,72,277,67,55,62,50,293,148,143,133,138,128,23,268,16,6,11,1,173,298,168,158,163,153,88,93,98,78,283,83,321,323,318,320,319,322,113,108,103,288,123,118,353,358,368,372,336,363,347,342,330,377,34,29,274,39,44,49,209,214,219,224,229,234,249,239,244,264,254,259,189,179,184,204,194,199,74,279,69,56,64,51,294,149,144,134,139,129,24,269,18,9,14,4,174,299,169,159,164,154,89,94,99,79,284,84,305,304,302,300,301,303,114,109,104,289,124,119,354,359,369,374,339,364,349,344,334,378,33,28,273,38,43,48,208,213,218,223,228,233,248,238,243,263,253,258,188,178,183,203,193,198,73,278,68,59,63,54,292,147,142,132,137,127,21,267,17,8,13,3,172,297,167,157,162,152,87,92,97,77,282,82,316,315,313,312,314,317,112,107,102,287,122,117,352,357,367,373,338,362,348,343,333,379 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, M = {69} 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 23:15:57 · history