Equation 677 Database

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Magma 8cd98d819ed1…

magma 8cd98d819ed1
Size
381
Isomorphism class hash
8cd98d819ed1c352604177f644d4f4a8c68e13a44fb058869b951f55e5994ab8
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 23:35:40
Display reorder
380,278,273,283,256,264,268,43,48,38,58,63,53,308,306,307,311,309,310,163,153,158,148,137,142,220,210,215,206,196,201,123,128,133,108,113,118,7,293,6,73,78,68,250,243,245,235,226,230,93,83,88,103,98,298,188,193,183,171,178,166,288,28,33,22,13,18,358,348,343,378,363,353,338,373,330,368,276,271,280,257,260,265,42,45,37,55,60,50,318,319,320,321,322,323,161,151,156,145,136,140,222,212,217,207,197,202,120,126,130,105,110,115,3,291,1,70,76,65,252,241,246,237,227,232,90,80,85,100,96,295,186,191,181,170,175,165,286,25,30,24,12,17,356,346,341,375,361,351,336,371,332,365,277,272,282,255,261,267,40,46,35,56,61,51,327,328,329,324,325,326,162,152,157,147,138,143,223,213,218,208,198,203,122,127,132,107,112,117,2,290,0,71,75,66,253,242,248,238,225,231,92,82,87,102,97,297,187,192,182,173,177,168,285,26,31,20,10,15,357,347,342,377,362,350,335,372,333,366,275,270,281,258,262,266,41,47,36,57,62,52,313,314,312,316,317,315,160,150,155,146,135,141,221,211,216,205,195,200,121,125,131,106,111,116,5,292,4,72,77,67,251,240,247,236,228,233,91,81,86,101,95,296,185,190,180,172,176,167,287,27,32,21,11,16,355,345,340,376,360,352,337,370,331,367,279,274,284,259,263,269,44,49,39,59,64,54,304,305,303,300,302,301,164,154,159,149,139,144,224,214,219,209,199,204,124,129,134,109,114,119,8,294,9,74,79,69,254,244,249,239,229,234,94,84,89,104,99,299,189,194,184,174,179,169,289,29,34,23,14,19,359,349,344,379,364,354,339,374,334,369 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, M = {67} 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 23:35:41 · history