Equation 677 Database

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Magma f37e3c8080fc…

magma f37e3c8080fc
Size
381
Isomorphism class hash
f37e3c8080fcf3fdbe892e0fae2baa594c6477a29f4077ad9a1f9b044ecf70b2
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 23:17:52
Display reorder
380,0,221,2,5,3,4,75,81,250,86,91,95,182,172,177,167,157,162,25,26,24,28,215,27,303,304,305,301,300,302,111,117,120,292,102,107,265,255,260,286,271,276,213,203,208,198,189,194,16,17,280,13,14,15,137,126,131,152,142,147,245,296,240,231,236,226,355,345,335,365,352,363,341,333,372,376,11,220,12,10,8,9,79,80,251,85,90,96,184,174,179,169,159,164,7,6,29,22,216,23,313,314,312,316,317,315,113,119,124,294,104,109,269,259,264,289,274,279,211,200,206,196,188,193,18,1,281,21,19,20,139,129,134,154,144,149,246,295,241,230,235,225,356,346,336,369,354,364,340,331,374,379,53,223,54,52,50,51,77,83,253,88,93,98,180,170,175,165,156,160,49,46,45,48,218,47,320,318,319,323,321,322,110,115,121,290,101,106,267,257,262,287,272,277,210,201,205,195,187,192,58,59,283,55,56,57,135,125,130,151,141,146,248,298,243,233,238,228,358,348,338,367,350,360,343,330,371,377,38,222,39,37,35,36,76,82,252,87,92,97,181,171,176,166,155,161,34,31,30,33,217,32,327,328,329,324,325,326,114,116,122,291,100,105,266,256,261,285,270,275,212,202,207,197,186,191,43,44,282,40,41,42,136,127,132,150,140,145,247,297,242,232,237,227,357,347,337,366,351,361,342,332,370,375,68,224,69,67,65,66,78,84,254,89,94,99,183,173,178,168,158,163,64,61,60,63,219,62,310,311,309,307,308,306,112,118,123,293,103,108,268,258,263,288,273,278,214,204,209,199,185,190,73,74,284,70,71,72,138,128,133,153,143,148,249,299,244,234,239,229,359,349,339,368,353,362,344,334,373,378 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, 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 23:17:53 · history