Equation 677 Database

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Magma 97f9d9d9bd13…

magma 97f9d9d9bd13
Size
381
Isomorphism class hash
97f9d9d9bd134be5752fa58ee1fa8dffa48960a91082f86be1f0ec215b42e481
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 23:26:48
Display reorder
380,37,42,38,39,40,41,201,206,1,275,285,296,265,240,245,250,255,260,210,216,221,226,231,236,30,271,281,291,28,29,314,315,316,311,312,313,43,44,45,46,47,48,161,166,140,145,150,156,186,191,196,170,175,180,35,36,31,32,33,34,49,54,50,51,52,53,357,334,361,371,339,353,369,337,349,377,11,10,12,7,8,9,203,207,110,277,287,297,267,242,247,252,257,262,212,217,222,227,232,237,27,270,280,290,25,26,321,322,324,326,328,319,16,17,18,13,14,15,162,167,142,147,152,157,187,192,197,172,177,182,0,2,3,4,5,6,22,21,23,24,19,20,359,338,360,370,343,352,366,335,347,376,106,105,107,108,103,104,200,209,138,278,288,298,268,243,248,253,258,263,213,218,223,228,233,238,82,273,283,293,83,84,303,304,305,301,300,302,87,88,89,90,85,86,163,168,143,148,153,158,188,193,198,173,178,183,100,101,102,97,98,99,93,92,94,95,96,91,358,330,362,373,341,351,367,345,346,378,71,70,72,73,74,75,204,208,139,279,289,299,269,244,249,254,259,264,214,219,224,229,234,239,62,272,282,292,63,61,320,323,325,327,329,318,78,79,80,81,76,77,164,169,144,149,154,159,189,194,199,174,179,184,66,67,68,69,64,65,55,60,56,57,58,59,355,332,363,372,344,354,368,340,342,379,132,131,133,134,129,130,202,205,109,276,286,295,266,241,246,251,256,261,211,215,220,225,230,235,137,274,284,294,135,136,306,307,308,309,310,317,113,114,115,116,111,112,160,165,141,146,151,155,185,190,195,171,176,181,126,127,128,123,124,125,119,118,120,121,122,117,356,331,364,374,336,350,365,348,333,375 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {71} 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 23:26:49 · history