Equation 677 Database

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Magma 45b65fcbf09b…

magma 45b65fcbf09b
Size
381
Isomorphism class hash
45b65fcbf09b21544e2238b268132f7802f2c950dfd23666b44104a51343f016
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 23:33:04
Display reorder
380,33,32,34,35,30,31,58,59,54,55,56,57,270,275,281,286,291,296,191,196,201,206,180,185,266,240,247,250,255,261,45,46,47,42,43,44,323,318,319,320,321,322,170,175,151,156,160,165,39,40,41,36,37,38,225,230,239,211,216,221,52,51,50,53,48,49,335,343,344,354,367,332,361,359,372,377,116,114,118,121,123,125,99,101,90,92,95,97,273,278,283,288,293,298,193,198,203,208,183,188,268,243,249,253,258,263,147,149,138,140,143,145,325,326,327,328,329,324,173,178,153,158,163,168,135,137,126,128,131,133,228,233,237,213,218,223,108,106,104,111,113,102,330,349,334,352,365,346,358,356,370,375,83,82,78,79,80,81,74,75,76,77,72,73,272,277,282,287,292,297,190,195,200,205,181,186,267,242,248,252,257,262,62,63,64,65,60,61,313,314,315,316,317,312,171,176,150,155,161,166,85,86,87,88,89,84,226,231,236,212,217,220,71,70,69,66,67,68,338,333,336,350,368,337,357,364,371,376,117,115,119,120,122,124,98,100,91,93,94,96,271,276,280,285,290,295,192,197,202,207,182,187,265,241,246,251,256,260,146,148,139,141,142,144,306,307,308,309,310,311,172,177,152,157,162,167,134,136,127,129,130,132,227,232,235,210,215,222,109,107,105,110,112,103,340,348,345,351,369,347,362,360,373,378,6,11,7,8,9,10,5,1,0,2,3,4,274,279,284,289,294,299,194,199,204,209,184,189,269,244,245,254,259,264,23,18,19,20,21,22,304,305,301,300,302,303,174,179,154,159,164,169,17,12,13,14,15,16,229,234,238,214,219,224,27,26,25,28,29,24,342,341,339,353,366,331,363,355,374,379 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#81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e, M = {70} 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 23:33:05 · history