Equation 677 Database

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Magma d2aee6245323…

magma d2aee6245323
Size
381
Isomorphism class hash
d2aee624532326f717f485a4ca2211632b263e9aaa6654bad74dac46c9459417
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 23:20:31
Display reorder
380,314,313,315,316,317,312,90,91,92,93,94,95,84,85,86,87,88,89,294,299,274,279,284,289,254,259,264,269,244,249,19,20,21,22,23,18,17,12,13,14,15,16,55,56,57,58,59,54,51,52,53,48,49,50,81,82,83,78,79,80,74,75,76,77,72,73,344,346,333,340,345,379,339,343,334,373,302,300,303,304,305,301,130,131,126,127,128,129,123,124,125,120,121,122,293,298,273,278,283,288,253,258,263,268,243,248,134,135,136,137,132,133,141,142,143,138,139,140,199,200,201,202,203,198,195,196,197,192,193,194,153,154,155,150,151,152,146,147,148,149,144,145,355,352,330,363,351,378,362,354,353,372,318,320,329,321,322,319,8,9,10,11,6,7,0,2,3,4,5,1,290,296,270,275,280,285,250,255,260,265,241,246,180,181,182,183,184,185,188,189,190,191,186,187,236,237,238,239,234,235,230,231,232,233,228,229,115,116,117,118,119,114,113,108,109,110,111,112,350,332,360,367,331,376,368,349,361,371,326,325,327,328,323,324,172,173,168,169,170,171,179,174,175,176,177,178,291,295,271,276,281,286,251,256,261,266,240,245,38,39,40,41,36,37,45,46,47,42,43,44,163,164,165,166,167,162,159,160,161,156,157,158,211,212,213,214,215,210,209,204,205,206,207,208,364,359,337,357,358,375,356,369,338,370,310,309,311,306,307,308,33,34,35,30,31,32,28,29,24,25,26,27,292,297,272,277,282,287,252,257,262,267,242,247,224,225,226,227,222,223,217,218,219,220,221,216,107,102,103,104,105,106,96,97,98,99,100,101,68,69,70,71,66,67,63,64,65,60,61,62,342,336,366,348,335,377,347,341,365,374 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {76} 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 23:20:32 · history