Equation 677 Database

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Magma 76e142da0d03…

magma 76e142da0d03
Size
381
Isomorphism class hash
76e142da0d030f6fa149b55a0631364f0221cc2cdc788cda83aefbf4800920cc
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 23:33:00
Display reorder
380,245,240,250,256,261,266,291,296,270,275,280,285,309,310,311,306,307,308,75,76,77,72,73,74,67,68,69,70,71,66,63,64,65,60,61,62,82,83,78,79,80,81,215,220,226,231,236,210,160,165,170,176,150,155,196,201,206,180,185,190,86,85,84,87,88,89,343,359,368,346,360,337,373,344,378,342,248,243,253,258,263,268,293,298,273,278,283,288,312,313,314,315,316,317,114,116,118,120,123,125,138,140,142,145,147,149,107,109,111,113,102,105,92,95,97,99,101,90,218,223,228,233,238,213,163,168,173,178,153,158,198,203,208,183,188,193,126,137,135,128,131,133,335,356,365,353,362,336,370,352,375,349,249,244,254,259,264,269,294,299,274,279,284,289,321,322,323,318,319,320,48,49,50,51,52,53,41,36,37,38,39,40,44,45,46,47,42,43,31,32,33,34,35,30,219,224,229,234,239,214,164,169,174,179,154,159,199,204,209,184,189,194,54,59,58,55,56,57,340,358,367,341,363,339,372,333,377,334,247,242,252,257,262,267,292,297,272,277,282,287,300,302,303,304,305,301,115,117,119,121,122,124,139,141,143,144,146,148,106,108,110,112,103,104,93,94,96,98,100,91,217,222,227,232,237,212,162,167,172,177,152,157,197,202,207,182,187,192,127,136,134,129,130,132,347,357,369,354,361,348,374,351,379,350,246,241,251,255,260,265,290,295,271,276,281,286,327,328,329,324,325,326,22,23,18,19,20,21,6,7,8,9,10,11,17,12,13,14,15,16,24,25,26,27,28,29,216,221,225,230,235,211,161,166,171,175,151,156,195,200,205,181,186,191,1,5,4,0,2,3,331,355,366,345,364,338,371,330,376,332 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#81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e, 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 23:33:01 · history