Equation 677 Database

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Magma 40613b8d033c…

magma 40613b8d033c
Size
381
Isomorphism class hash
40613b8d033c1c7750720564eff7e04ca658139ca55d2d13fd672f3ea4dd3ef3
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 23:30:35
Display reorder
380,302,168,161,142,155,129,175,148,122,135,303,169,156,143,150,136,130,176,149,123,304,170,157,138,151,137,131,177,144,124,305,171,158,139,152,132,126,178,145,125,301,172,159,140,153,133,127,179,146,120,173,134,300,160,141,154,128,174,147,121,167,163,164,165,166,162,347,377,350,369,368,378,379,348,349,367,316,25,12,58,6,45,32,5,38,51,320,26,13,59,7,52,46,33,1,39,324,27,14,54,8,53,47,34,0,40,328,28,15,55,9,48,42,35,2,41,308,29,16,56,10,49,43,30,3,36,24,50,313,17,57,11,44,31,4,37,18,20,21,22,23,19,357,330,355,332,353,352,354,356,351,331,326,119,106,73,86,60,112,93,67,80,307,114,107,74,87,81,61,113,94,68,312,115,102,75,88,82,62,108,95,69,314,116,103,76,89,83,63,109,90,70,318,117,104,77,84,78,64,110,91,71,118,79,322,105,72,85,65,111,92,66,98,100,101,96,97,99,375,346,343,366,365,342,344,345,364,376,306,280,265,250,261,297,282,256,289,243,311,281,266,251,258,244,298,283,257,290,315,276,267,246,262,245,299,284,252,291,319,277,268,247,263,240,294,285,253,292,323,278,269,248,259,241,295,286,254,293,279,242,327,264,249,260,296,287,255,288,272,274,275,270,271,273,340,341,373,372,360,363,361,339,374,362,309,199,186,218,231,205,192,238,212,225,310,200,187,219,232,226,206,193,239,213,317,201,188,220,233,227,207,194,234,214,321,202,189,221,228,222,208,195,235,215,325,203,190,216,229,223,209,196,236,210,198,224,329,191,217,230,204,197,237,211,184,180,181,182,183,185,371,338,370,358,335,334,336,337,333,359 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#74c2b3c081debeba123eb77544690d7ded5a1824946fccb13e95b8196af8499d, M = {66} 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 23:30:36 · history