Equation 677 Database

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Magma 6d7f53a03878…

magma 6d7f53a03878
Size
381
Isomorphism class hash
6d7f53a038782dea8d71488591187e165c7b3c29004f3d27a1a4ac31a4f947fc
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 23:31:43
Display reorder
380,27,28,29,30,32,47,33,45,31,46,135,140,136,137,138,142,144,143,139,141,185,192,186,187,188,189,194,190,191,193,236,242,235,237,238,239,244,240,241,243,310,308,311,309,312,90,85,86,87,88,92,94,93,89,91,292,287,285,288,289,286,294,290,291,293,307,342,339,375,346,374,338,341,343,376,347,10,38,39,11,9,34,36,49,48,35,111,146,112,113,114,110,145,147,148,149,161,196,162,163,164,160,195,197,198,199,212,246,211,213,214,210,245,247,248,249,313,301,314,324,302,97,61,62,63,64,60,95,96,99,98,296,262,261,263,264,260,295,297,299,298,325,360,379,361,377,333,335,340,378,349,348,23,24,25,26,44,17,41,19,40,18,131,122,132,133,134,130,120,124,123,121,181,172,182,183,184,180,170,174,173,171,232,222,231,233,234,230,220,224,223,221,317,318,319,320,321,72,81,82,83,84,80,70,74,73,71,273,282,281,283,284,280,270,274,272,271,322,372,367,373,364,353,352,351,365,350,366,21,20,43,42,22,3,0,37,1,2,126,103,125,129,128,127,104,100,102,101,176,153,175,178,179,177,154,150,152,151,225,203,226,229,228,227,204,200,202,201,329,300,327,326,328,53,76,75,79,78,77,54,50,52,51,253,275,276,279,278,277,254,252,250,251,323,371,355,370,354,368,356,344,357,369,345,4,5,6,7,8,12,13,14,16,15,105,118,106,107,108,109,115,116,117,119,155,168,156,157,158,159,165,166,167,169,206,218,205,207,208,209,215,216,217,219,303,315,304,316,305,68,55,56,57,58,59,65,66,67,69,268,256,255,257,258,259,265,266,267,269,306,334,332,358,363,336,331,337,362,359,330 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#7d1ca7f19a6476d5d19958a01b2b150bc7a0c60d280d02593b805c82a69bb42e, M = {76} 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 23:31:43 · history