Equation 677 Database

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Magma 25356b85a791…

magma 25356b85a791
Size
381
Isomorphism class hash
25356b85a7919bf5174471d815e630edd601cc97fbe3d766c6576bfd7ef2435d
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 23:47:54
Display reorder
380,114,115,229,113,111,112,199,204,209,184,189,194,279,269,274,299,280,289,239,244,249,254,259,264,104,105,103,107,219,106,119,294,118,116,117,234,179,169,174,164,154,159,124,129,133,139,144,149,108,109,224,5,4,110,300,301,302,303,304,305,99,98,100,101,102,214,339,364,349,369,359,353,334,344,374,379,72,71,227,68,69,70,197,202,207,182,187,192,276,267,272,296,281,285,235,240,248,252,257,262,58,59,60,61,217,62,21,290,20,19,22,231,175,165,170,161,151,156,121,127,134,135,140,145,67,66,222,65,63,64,328,327,329,324,325,326,57,53,54,55,56,212,337,360,347,366,356,350,333,342,371,378,45,44,226,47,48,46,195,201,206,181,186,191,275,265,270,297,283,287,236,241,245,251,256,261,9,10,8,7,216,6,49,292,50,51,52,232,177,167,172,162,152,157,122,126,131,137,142,147,37,38,220,34,35,36,321,323,322,320,318,319,24,23,25,26,27,210,335,362,345,367,357,354,331,341,372,376,97,96,228,93,94,95,198,203,208,183,188,193,278,268,273,298,284,288,237,242,246,250,255,260,83,84,85,86,218,87,15,291,16,17,18,230,178,168,173,163,153,158,123,128,132,138,143,148,92,91,223,90,88,89,306,308,307,311,309,310,82,78,79,80,81,213,338,363,348,368,355,352,332,343,373,375,43,73,225,42,40,41,196,200,205,180,185,190,277,266,271,295,282,286,238,243,247,253,258,263,30,31,29,33,215,32,77,293,76,74,75,233,176,166,171,160,150,155,120,125,130,136,141,146,3,2,221,0,1,39,314,313,312,316,317,315,14,13,12,11,28,211,336,361,346,365,358,351,330,340,370,377 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 = {68} 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 23:47:55 · history