Equation 677 Database

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Magma 18ff6ed9d732…

magma 18ff6ed9d732
Size
381
Isomorphism class hash
18ff6ed9d7328f8c636eb789831b5073a3450a527ce485b580ba7c015d16ea7f
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 23:43:11
Display reorder
380,90,87,98,101,280,106,156,150,296,172,161,166,46,35,40,56,51,270,115,121,110,1,286,0,30,266,25,15,21,10,200,191,196,185,175,182,305,303,304,302,301,300,230,221,226,215,205,213,125,130,291,141,146,136,275,61,66,70,75,81,245,240,236,256,261,251,356,370,331,340,361,345,350,366,336,375,92,86,95,102,282,107,157,152,297,171,160,167,47,37,42,57,52,273,117,122,112,5,287,4,32,267,27,17,20,12,202,192,197,187,178,183,316,317,315,313,314,312,232,222,227,217,207,210,127,132,292,142,147,137,277,62,67,72,77,82,247,242,237,257,262,252,357,372,332,342,362,347,352,367,337,379,91,88,97,100,281,105,155,151,295,173,162,165,45,36,41,55,50,271,116,120,111,3,285,2,31,265,26,16,24,11,201,190,195,186,177,181,311,309,310,308,306,307,231,220,225,216,208,212,126,131,290,140,145,135,276,60,65,71,76,80,246,241,235,255,260,250,355,371,330,341,360,346,351,365,335,376,93,85,96,103,283,108,158,153,298,170,163,168,48,38,43,58,53,272,118,123,113,7,288,6,33,268,28,18,22,13,203,193,198,188,176,180,318,319,320,321,322,323,233,223,228,218,206,211,128,133,293,143,148,138,278,63,68,73,78,83,248,243,238,258,263,253,358,373,333,343,363,348,353,368,338,377,94,89,99,104,284,109,159,154,299,174,164,169,49,39,44,59,54,274,119,124,114,9,289,8,34,269,29,19,23,14,204,194,199,189,179,184,328,326,327,325,324,329,234,224,229,219,209,214,129,134,294,144,149,139,279,64,69,74,79,84,249,244,239,259,264,254,359,374,334,344,364,349,354,369,339,378 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, M = {74} 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 23:43:12 · history