Equation 677 Database

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Magma 5e56a436529a…

magma 5e56a436529a
Size
381
Isomorphism class hash
5e56a436529a1bbf4339bce97825a9052dee31d698ca151260faf07008306e51
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 23:36:54
Display reorder
380,4,292,5,147,142,17,267,12,32,20,25,137,196,200,191,182,185,177,157,297,152,172,162,167,270,36,41,46,51,55,281,101,105,96,86,91,235,242,247,251,256,261,120,126,131,111,116,285,66,71,61,275,80,75,315,316,317,312,313,314,225,231,220,210,215,206,370,355,362,331,367,340,351,337,345,377,0,290,2,145,140,16,265,11,30,21,29,135,197,202,192,180,186,175,155,296,150,171,160,166,271,35,40,45,52,56,280,100,106,95,85,90,237,240,245,252,257,262,121,125,130,110,115,286,65,70,60,276,81,76,324,325,326,327,328,329,227,232,222,212,217,207,372,356,360,332,366,341,350,335,346,376,1,291,3,146,141,15,266,10,34,22,28,136,195,201,190,181,188,176,156,295,151,170,161,165,272,37,42,47,53,57,282,102,107,97,87,92,236,241,246,250,255,260,122,127,132,112,117,287,67,72,62,277,82,77,308,310,306,302,304,300,226,230,221,211,216,205,371,357,361,330,365,342,352,336,347,375,6,293,7,148,143,18,268,13,33,23,27,138,198,203,193,183,187,178,158,298,153,173,163,168,273,38,43,48,54,58,283,103,108,98,88,93,238,243,248,253,258,263,123,128,133,113,118,288,68,73,63,278,83,78,319,320,318,322,323,321,228,233,223,213,218,208,373,358,363,333,368,343,353,338,348,378,9,294,8,149,144,19,269,14,31,24,26,139,199,204,194,184,189,179,159,299,154,174,164,169,274,39,44,49,50,59,284,104,109,99,89,94,239,244,249,254,259,264,124,129,134,114,119,289,69,74,64,279,84,79,309,311,307,303,305,301,229,234,224,214,219,209,374,359,364,334,369,344,354,339,349,379 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, M = {69} 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 23:36:55 · history