Equation 677 Database

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Magma bc5968e057a8…

magma bc5968e057a8
Size
381
Isomorphism class hash
bc5968e057a8f1c48af4baff70f294d79dfee69c64ad3d90b7190c8c223f50bd
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 23:38:58
Display reorder
380,203,198,193,183,188,178,243,248,238,257,263,253,153,158,298,168,173,163,17,267,12,32,24,27,218,208,213,233,223,228,272,37,42,47,52,57,281,102,107,96,86,91,112,117,287,120,125,132,70,61,65,80,76,275,138,143,148,6,7,293,325,324,326,327,328,329,357,373,368,332,351,363,342,345,337,378,202,197,192,182,187,177,240,245,235,258,260,250,152,157,297,167,172,162,18,268,13,33,22,28,217,207,212,232,222,227,273,38,43,48,53,58,283,103,108,98,88,93,113,118,288,123,128,133,73,63,68,83,78,278,137,142,147,4,5,292,306,308,307,311,309,310,358,372,367,333,352,362,343,348,338,377,200,196,190,181,186,175,242,246,237,255,261,252,151,156,295,165,170,161,15,266,10,30,21,26,216,206,211,230,220,225,271,35,40,45,51,56,280,100,106,97,87,92,110,115,286,122,126,130,71,60,67,82,77,277,136,141,146,1,3,291,323,322,321,319,320,318,355,370,365,330,350,361,341,347,336,375,201,195,191,180,185,176,241,247,236,256,262,251,150,155,296,166,171,160,16,265,11,31,20,25,215,205,210,231,221,226,270,36,41,46,50,55,282,101,105,95,85,90,111,116,285,121,127,131,72,62,66,81,75,276,135,140,145,0,2,290,317,316,315,313,314,312,356,371,366,331,354,360,340,346,335,376,204,199,194,184,189,179,244,249,239,259,264,254,154,159,299,169,174,164,19,269,14,34,23,29,219,209,214,234,224,229,274,39,44,49,54,59,284,104,109,99,89,94,114,119,289,124,129,134,74,64,69,84,79,279,139,144,149,8,9,294,305,304,303,300,302,301,359,374,369,334,353,364,344,349,339,379 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#a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f, M = {72} 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 23:38:59 · history