Equation 677 Database

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Magma 01cef59d22ba…

magma 01cef59d22ba
Size
399
Isomorphism class hash
01cef59d22ba80d48288287929794c9a6ba4725d0d0ca14f28e4b9b54dcb1cf4
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-09 01:18:15
Display reorder
234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,381,231,252,191,203,232,253,192,204,233,254,193,205,225,255,194,206,226,256,195,198,227,257,196,199,228,258,197,200,229,259,189,201,230,260,190,202,261,184,224,212,262,185,216,213,263,186,217,214,264,187,218,215,265,188,219,207,266,180,220,208,267,181,221,209,268,182,222,210,269,183,223,211,392,386,385,391,178,83,297,333,179,84,298,334,171,85,299,335,172,86,300,336,173,87,301,337,174,88,302,338,175,89,303,339,176,81,304,340,177,82,305,341,76,290,162,326,77,291,163,327,78,292,164,328,79,293,165,329,80,294,166,330,72,295,167,331,73,296,168,332,74,288,169,324,75,289,170,325,384,390,389,383,306,63,281,96,307,64,282,97,308,65,283,98,309,66,284,90,310,67,285,91,311,68,286,92,312,69,287,93,313,70,279,94,314,71,280,95,56,274,315,105,57,275,316,106,58,276,317,107,59,277,318,99,60,278,319,100,61,270,320,101,62,271,321,102,54,272,322,103,55,273,323,104,387,398,397,388,160,50,349,342,161,51,351,344,153,52,353,346,154,53,355,348,155,45,357,350,156,46,359,352,157,47,343,354,158,48,345,356,159,49,347,358,43,367,144,360,44,369,145,362,36,371,146,364,37,373,147,366,38,375,148,368,39,376,149,370,40,361,150,372,41,363,151,374,42,365,152,377,393,395,396,394,119,6,132,24,120,7,133,25,121,8,134,26,122,1,126,18,123,0,127,19,124,2,128,20,125,3,129,21,117,4,130,22,118,5,131,23,15,141,112,33,16,142,113,34,17,143,114,35,9,135,115,27,10,136,116,28,11,137,108,29,12,138,109,30,13,139,110,31,14,140,111,32,380,382,379,378 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 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#75d384d348acb1d156178512c9b71aa59bbe5f2768da083599caf5b863fa7f88, M = the submagma generated by {0} (19 elements) 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: 21.

last edited by qawbecrdtey at 2026-10-09 01:18:16 · history