Equation 677 Database

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Magma 162fb0289af6…

magma 162fb0289af6
Size
381
Isomorphism class hash
162fb0289af67580ee2bb6ded1846d506870610db6bd2fc628dfb859d74024e5
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 23:48:25
Display reorder
380,236,231,226,215,220,210,285,82,76,92,99,89,241,246,250,256,261,266,176,166,170,160,151,155,206,195,200,191,182,187,291,105,100,116,120,111,130,135,126,146,295,141,328,329,327,325,326,324,275,30,26,40,45,35,10,20,16,7,2,272,281,50,55,61,66,70,346,360,335,340,330,356,366,350,375,371,235,230,225,216,221,211,289,81,79,90,97,87,244,249,254,255,260,265,175,165,171,161,150,156,205,196,201,190,181,186,294,109,104,119,124,114,134,139,129,149,299,144,300,302,301,304,305,303,279,32,29,41,46,36,14,24,18,9,4,274,284,54,59,64,69,74,349,364,338,344,334,359,365,354,376,370,239,234,229,219,224,214,288,84,78,94,96,85,240,245,253,259,264,269,179,169,174,164,154,159,209,199,204,194,184,189,293,108,103,118,123,113,133,138,128,148,298,143,315,316,317,312,313,314,278,34,28,44,49,39,13,23,17,8,3,273,283,53,58,63,68,73,348,363,337,343,333,358,369,353,379,374,238,233,228,218,223,213,287,83,77,93,95,86,242,247,251,257,262,267,178,168,173,163,153,158,208,198,203,193,180,185,292,107,102,117,122,112,132,137,127,147,297,142,309,310,311,306,307,308,277,33,27,43,48,38,11,22,19,5,1,271,282,52,57,62,67,72,347,362,336,342,331,357,368,352,378,373,237,232,227,217,222,212,286,80,75,91,98,88,243,248,252,258,263,268,177,167,172,162,152,157,207,197,202,192,183,188,290,106,101,115,121,110,131,136,125,145,296,140,322,323,321,319,320,318,276,31,25,42,47,37,12,21,15,6,0,270,280,51,56,60,65,71,345,361,339,341,332,355,367,351,377,372 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 = {75} 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 23:48:26 · history