Equation 677 Database

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Magma bcb20e2f12fc…

magma bcb20e2f12fc
Size
381
Isomorphism class hash
bcb20e2f12fc1267fc191e5bdac8c787e363f38f4d08d14b93abf82143fc16a9
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 23:24:26
Display reorder
380,262,257,252,242,247,237,85,76,80,96,91,280,179,180,185,191,195,200,61,65,70,276,50,55,164,154,159,299,169,174,147,292,142,131,136,126,316,317,315,313,314,312,273,49,44,34,38,26,106,111,100,286,120,115,227,222,232,207,212,217,1,6,17,267,12,20,340,372,369,346,362,350,337,356,332,378,263,258,253,243,248,238,88,78,83,98,93,283,175,181,186,190,196,204,63,68,73,278,53,58,161,151,156,295,165,170,148,293,143,133,138,128,311,309,310,308,306,307,270,45,41,31,35,28,108,113,103,288,123,118,228,223,233,208,213,218,3,7,18,268,10,23,343,373,365,348,363,353,338,358,333,379,260,255,250,240,245,236,87,77,82,97,92,282,176,183,187,193,198,201,62,67,72,277,52,57,160,150,155,296,166,171,145,291,140,130,135,127,325,326,324,328,329,327,272,47,42,32,37,25,107,112,102,287,122,117,226,221,231,206,211,215,2,9,16,266,13,21,342,371,366,347,361,352,336,357,330,375,264,259,254,244,249,239,89,79,84,99,94,284,178,184,189,194,199,203,64,69,74,279,54,59,163,153,158,298,168,173,149,294,144,134,139,129,304,305,303,300,302,301,271,46,40,30,36,29,109,114,104,289,124,119,229,224,234,209,214,219,4,8,19,269,11,24,344,374,368,349,364,354,339,359,334,377,261,256,251,241,246,235,86,75,81,95,90,281,177,182,188,192,197,202,60,66,71,275,51,56,162,152,157,297,167,172,146,290,141,132,137,125,320,318,319,323,321,322,274,48,43,33,39,27,105,110,101,285,121,116,225,220,230,205,210,216,0,5,15,265,14,22,341,370,367,345,360,351,335,355,331,376 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#4b20d49131fa1763d6463a102f127bf88ae35086a2437318b417535ceb91dad1, M = {72} 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 23:24:26 · history