Equation 677 Database

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Magma 3b6c4425a7f2…

magma 3b6c4425a7f2
Size
381
Isomorphism class hash
3b6c4425a7f21f9c342371387f5f5743aad55bfe4d2a6adcda161b03798ce81a
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 23:22:35
Display reorder
380,320,319,318,322,323,321,143,133,138,158,148,153,268,272,263,283,288,278,43,44,228,40,41,42,198,203,193,213,218,208,108,113,103,123,128,118,38,223,39,35,36,37,298,78,83,88,93,98,53,58,61,68,293,73,178,183,188,163,168,173,233,243,238,258,248,253,352,333,338,358,363,368,348,343,373,378,316,315,317,312,313,314,144,134,139,159,149,154,269,274,264,284,289,279,9,10,229,12,13,11,199,204,194,214,219,209,109,114,104,124,129,119,49,224,48,46,47,45,299,79,84,89,94,99,54,59,63,69,294,74,179,184,189,164,169,174,234,244,239,259,249,254,353,334,339,359,364,369,349,344,374,379,308,307,306,310,311,309,141,131,136,155,145,150,265,270,260,280,285,275,17,18,225,14,15,16,196,201,191,211,216,206,106,111,101,120,125,115,33,222,32,30,31,34,295,76,81,86,91,95,50,57,62,66,290,71,175,180,185,161,166,171,231,241,236,256,245,250,350,331,337,356,360,366,345,340,370,376,305,304,303,300,302,301,140,130,135,156,146,151,266,271,261,281,286,276,7,8,226,4,5,6,195,200,190,210,215,205,105,110,100,121,126,116,23,220,22,20,21,19,296,75,80,85,90,96,52,55,64,65,291,70,176,181,186,160,165,170,230,240,235,255,246,251,351,330,335,355,361,365,346,341,371,375,325,324,326,327,328,329,142,132,137,157,147,152,267,273,262,282,287,277,28,29,227,25,26,27,197,202,192,212,217,207,107,112,102,122,127,117,1,221,24,0,2,3,297,77,82,87,92,97,51,56,60,67,292,72,177,182,187,162,167,172,232,242,237,257,247,252,354,332,336,357,362,367,347,342,372,377 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, M = {66} 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 23:22:36 · history