Equation 677 Database

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Magma e88d8a12f992…

magma e88d8a12f992
Size
399
Isomorphism class hash
e88d8a12f9921de20f7d6c81cdad5b64b541c55d00bfd682bd1e6391830f4b8b
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
2026-10-07 18:35:30
Display reorder
266,267,268,269,261,262,263,264,265,259,260,252,253,254,255,256,257,258,378,327,285,292,318,328,319,286,293,329,320,287,294,330,321,279,295,331,322,280,296,332,323,281,288,282,324,315,289,325,316,283,290,326,317,284,291,311,336,278,301,312,337,270,302,313,338,271,303,314,339,272,304,306,340,273,305,307,341,274,297,308,333,275,298,309,334,276,299,310,335,277,300,391,385,386,392,202,109,96,188,203,180,110,97,204,181,111,98,205,182,112,90,206,183,113,91,198,184,114,92,115,199,185,93,200,186,116,94,201,187,108,95,197,211,118,105,189,212,119,106,190,213,120,107,191,214,121,99,192,215,122,100,193,207,123,101,194,208,124,102,195,209,125,103,196,210,117,104,383,389,390,384,35,88,137,217,27,218,89,138,28,219,81,139,29,220,82,140,30,221,83,141,31,222,84,142,85,32,223,143,33,224,86,135,34,216,87,136,226,19,72,130,227,20,73,131,228,21,74,132,229,22,75,133,230,23,76,134,231,24,77,126,232,25,78,127,233,26,79,128,225,18,80,129,388,398,397,387,349,67,342,174,350,175,68,344,352,176,69,346,354,177,70,348,356,178,71,351,358,179,63,353,64,343,171,355,345,172,65,357,347,173,66,359,167,367,60,360,168,368,61,362,169,370,62,364,170,372,54,366,162,374,55,369,163,376,56,371,164,361,57,373,165,363,58,375,166,365,59,377,394,395,396,393,240,17,149,51,241,52,9,150,242,53,10,151,234,45,11,152,235,46,12,144,236,47,13,145,14,237,48,146,238,49,15,147,239,50,16,148,44,249,0,158,36,250,2,159,37,251,3,160,38,243,4,161,39,244,5,153,40,245,6,154,41,246,7,155,42,247,8,156,43,248,1,157,382,379,381,380 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#c60f2b3644ea94996586b120816e03201d0b2e4eb5985db9ba99dad7f9628d7f, 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 2026-10-07 18:35:31 · history