Equation 677 Database

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Magma 4f55de38278f…

magma 4f55de38278f
Size
381
Isomorphism class hash
4f55de38278f18e0cf6bc1710bf33158e8d1791255a71f5b978a9e7fa98f8d16
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 23:37:42
Display reorder
380,255,265,260,251,240,247,155,161,150,171,176,166,181,187,191,195,200,205,34,38,26,275,46,41,101,106,111,115,120,291,320,318,319,323,321,322,214,219,224,228,234,239,60,65,71,280,51,56,130,296,125,140,145,135,285,81,76,90,95,85,272,2,7,10,16,20,335,350,356,376,345,341,330,369,361,371,257,267,262,252,242,248,156,160,151,170,175,165,182,186,192,196,201,206,32,37,27,277,47,42,102,107,112,117,122,292,312,313,314,315,316,317,210,215,220,226,232,238,62,67,72,282,52,57,132,297,127,142,147,137,287,82,77,92,97,87,270,0,6,12,15,21,336,352,357,375,347,342,332,366,362,370,256,266,261,250,241,246,157,162,152,172,177,167,183,188,193,197,202,207,33,39,25,276,45,40,100,105,110,116,121,290,324,325,326,327,328,329,211,216,221,227,233,237,61,66,70,281,50,55,131,295,126,141,146,136,286,80,75,91,96,86,271,1,5,13,19,22,338,351,355,377,346,340,331,365,360,372,259,269,264,254,244,249,159,164,154,174,179,169,180,185,190,198,203,208,31,35,29,279,49,44,104,109,114,119,124,294,302,301,300,305,303,304,212,217,222,225,231,235,64,69,74,284,54,59,134,299,129,144,149,139,289,84,79,94,99,89,274,4,9,14,18,24,339,354,359,379,349,344,334,368,364,374,258,268,263,253,243,245,158,163,153,173,178,168,184,189,194,199,204,209,30,36,28,278,48,43,103,108,113,118,123,293,308,306,307,311,309,310,213,218,223,229,230,236,63,68,73,283,53,58,133,298,128,143,148,138,288,83,78,93,98,88,273,3,8,11,17,23,337,353,358,378,348,343,333,367,363,373 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, 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 23:37:43 · history